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A226311
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a(n+5) = a(n+4)+a(n+3)+a(n+2)+a(n+1)+2*a(n) with a(0)=2, a(1)=1, a(2)=5, a(3)=10, a(4)=20.
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1
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2, 1, 5, 10, 20, 40, 77, 157, 314, 628, 1256, 2509, 5021, 10042, 20084, 40168, 80333, 160669, 321338, 642676, 1285352, 2570701, 5141405, 10282810, 20565620, 41131240, 82262477, 164524957, 329049914, 658099828, 1316199656, 2632399309, 5264798621, 10529597242, 21059194484, 42118388968, 84236777933, 168473555869
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OFFSET
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0,1
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LINKS
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FORMULA
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G.f.: (2*x^4+2*x^3+2*x^2-x+2) / ((1-2*x)*(x^4+x^3+x^2+x+1)). - Colin Barker, Jun 08 2013
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MAPLE
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f:=proc(n) option remember;
if n=0 then 2 elif n=1 then 1 elif n=2 then 5 elif n=3 then 10 elif n=4 then 20 else
f(n-1)+f(n-2)+f(n-3)+f(n-4)+2*f(n-5); fi; end;
[seq(f(n), n=0..40)];
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MATHEMATICA
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CoefficientList[Series[-(2 x^4 + 2 x^3 + 2 x^2 - x + 2) / ((2 x - 1) (x^4 + x^3 + x^2 + x + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 19 2013 *)
LinearRecurrence[{1, 1, 1, 1, 2}, {2, 1, 5, 10, 20}, 20] (* Harvey P. Dale, Jan 20 2015 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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