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A105754
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Lucas 8-step numbers.
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14
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1, 3, 7, 15, 31, 63, 127, 255, 502, 1003, 2003, 3999, 7983, 15935, 31807, 63487, 126719, 252936, 504869, 1007735, 2011471, 4014959, 8013983, 15996159, 31928831, 63730943, 127208950, 253913031, 506818327, 1011625183, 2019235407
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = Sum_{k=1..8} a(n-k) for n > 0, a(0)=8, a(n)=-1 for n=-7..-1.
G.f.: -x*(1 + 2*x + 3*x^2 + 4*x^3 + 5*x^4 + 6*x^5 + 7*x^6 + 8*x^7)/( -1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 ). - R. J. Mathar, Jun 20 2011
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MATHEMATICA
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a={-1, -1, -1, -1, -1, -1, -1, 8}; Table[s=Plus@@a; a=RotateLeft[a]; a[[ -1]]=s, {n, 50}]
CoefficientList[Series[-x*(1 + 2*x + 3*x^2 + 4*x^3 + 5*x^4 + 6*x^5 + 7*x^6 + 8*x^7 + 9*x^8)/(-1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9), {x, 0, 50}], x] (* G. C. Greubel, Dec 18 2017 *)
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PROG
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(PARI) a(n)=([0, 1, 0, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0, 0; 0, 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 0, 1, 0, 0, 0; 0, 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 0, 1; 1, 1, 1, 1, 1, 1, 1, 1]^(n-1)*[1; 3; 7; 15; 31; 63; 127; 255])[1, 1] \\ Charles R Greathouse IV, Jun 14 2015
(PARI) x='x+O('x^30); Vec(-x*(1 + 2*x + 3*x^2 + 4*x^3 + 5*x^4 + 6*x^5 + 7*x^6 + 8*x^7 + 9*x^8)/(-1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9)) \\ G. C. Greubel, Dec 18 2017
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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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