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A173033
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Second diagonal under the main diagonal in A172119 written in a square (see comment).
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18
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1, 4, 12, 28, 60, 124, 252, 508, 1020, 2044, 4092, 8188, 16380, 32764, 65532, 131068, 262140, 524284, 1048572, 2097148, 4194300, 8388604, 16777212, 33554428, 67108860, 134217724, 268435452, 536870908, 1073741820, 2147483644, 4294967292, 8589934588, 17179869180
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OFFSET
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0,2
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COMMENTS
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The Granvik array of A172119 is here written in "square": 1 :: 1 :: 1 :: 1 :: 1 :: 1 :: 1 :: 1 :: 1 :: 1 // 1 :: 2 :: 2 :: 2 :: 2 :: 2 :: 2 :: 2 :: 2 :: 2 // 1 :: 3 :: 4 :: 4 :: 4 :: 4 :: 4 :: 4 :: 4 :: 4 // 1 :: 4 :: 7 :: 8 :: 8 :: 8 :: 8 :: 8 :: 8 :: 8 // 1 :: 5 :: 12 :: 15 :: 16 :: 16 :: 16 :: 16 :: 16 :: 16 // 1 :: 6 :: 20 :: 28 :: 31 :: 32 :: 32 :: 32 :: 32 :: 32 // 1 :: 7 :: 33 :: 52 :: 60 :: 63 :: 64 :: 64 :: 64 :: 64 // 1 :: 8 :: 54 :: 96 :: 116 :: 124 :: 127 :: 128 :: 128 :: 128 // 1 :: 9 :: 88 :: 177 :: 224 :: 244 :: 252 :: 255 :: 256 :: 256 //
For n>0 a(n) is also the number of ways to place n^2 non-attacking kings on a 2n X 2n toroidal chessboard. - Vaclav Kotesovec, Aug 28 2011
The number of n-step self-avoiding walks on a 2D square lattice where no step is to a lattice point closer to the origin than the current point. - Scott R. Shannon, Dec 15 2023
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LINKS
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FORMULA
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G.f.: 4/(1-2*x) - 4/(1-x) + 1.
a(n) = 2^(n+2) - 4 for n>=1, a(0)=1.
a(n) = 2*a(n-1) + 4 for n>1. - J. Conrad, Nov 01 2015
a(n) = 3*a(n-1)-2*a(n-2) for n>2. - Colin Barker, Nov 03 2015
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EXAMPLE
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a(3) = 2^5 - 4 = 32 - 4 = 28.
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MAPLE
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taylor(4/(1-2*z)-4/(1-z)+1, z=0, 31);
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MATHEMATICA
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CoefficientList[Series[4 / (1 - 2 x) - 4 / (1 - x) + 1, {x, 0, 60}], x] (* Vincenzo Librandi, May 29 2013 *)
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PROG
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(PARI) x='x+O('x^50); Vec(4/(1-2*x)-4/(1-x)+1) \\ Altug Alkan, Nov 02 2015
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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