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A054569
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a(n) = 4*n^2 - 6*n + 3.
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50
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1, 7, 21, 43, 73, 111, 157, 211, 273, 343, 421, 507, 601, 703, 813, 931, 1057, 1191, 1333, 1483, 1641, 1807, 1981, 2163, 2353, 2551, 2757, 2971, 3193, 3423, 3661, 3907, 4161, 4423, 4693, 4971, 5257, 5551, 5853, 6163, 6481, 6807, 7141, 7483, 7833, 8191
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OFFSET
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1,2
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COMMENTS
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Move in 1-7 direction in a spiral organized like A068225 etc.
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LINKS
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FORMULA
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a(n+1) = 4*n^2 + 2*n + 1. - Paul Barry, Apr 02 2003
a(n) = 4*n^2 - 6*n+3 - 3*0^n (with leading zero). - Paul Barry, Jun 11 2003
Binomial transform of [1, 6, 8, 0, 0, 0, ...]. - Gary W. Adamson, Dec 28 2007
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: x*(1+x)*(1+3*x)/(1-x)^3. (End)
E.g.f.: -3 + (3 - 2*x + 4*x^2)*exp(x). - G. C. Greubel, Jul 04 2019
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {1, 7, 21}, 50] (* Harvey P. Dale, Nov 17 2012 *)
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PROG
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(Magma) [4*n^2-6*n+3: n in [1..50]]; // G. C. Greubel, Jul 04 2019
(Sage) [4*n^2-6*n+3 for n in (1..50)] # G. C. Greubel, Jul 04 2019
(GAP) List([1..50], n-> 4*n^2-6*n+3) # G. C. Greubel, Jul 04 2019
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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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EXTENSIONS
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STATUS
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approved
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