A251742 -id:A251742 - cp's OEIS frontend

A251672 8-step Fibonacci sequence starting with 0,0,0,0,0,0,1,0.

0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 4, 8, 16, 32, 64, 127, 254, 507, 1012, 2020, 4032, 8048, 16064, 32064, 64001, 127748, 254989, 508966, 1015912, 2027792, 4047536, 8079008, 16125952, 32187903, 64248058, 128241127, 255973288, 510930664, 1019833536, 2035619536

Offset: 0

Arie Bos, Dec 06 2014

a(n+8) equals the number of n-length binary words avoiding runs of 0's of lengths 8i+7, (i=0,1,2,...). - Milan Janjic, Feb 26 2015

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,1,1,1,1).

Other 8-step Fibonacci sequences are A079262, A105754, A251740, A251741, A251742, A251744, A251745.

LinearRecurrence[Table[1, {8}], {0, 0, 0, 0, 0, 0, 1, 0}, 43] (* Michael De Vlieger, Dec 09 2014 *)

a(n+8) = a(n) +a(n+1) +a(n+2) +a(n+3) +a(n+4) +a(n+5) +a(n+6) +a(n+7).
G.f.: x^6*(x-1)/(-1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8) . - R. J. Mathar, Mar 28 2025
a(n) = A079262(n+1)-A079262(n). - R. J. Mathar, Mar 28 2025

A251740 8-step Fibonacci sequence starting with 0,0,0,0,0,1,0,0.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 4, 8, 16, 32, 63, 126, 252, 503, 1004, 2004, 4000, 7984, 15936, 31809, 63492, 126732, 252961, 504918, 1007832, 2011664, 4015344, 8014752, 15997695, 31931898, 63737064, 127221167, 253937416, 506867000, 1011722336, 2019429328

Offset: 0

Arie Bos, Dec 07 2014

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,1,1,1,1)

Other 8-step Fibonacci sequences are A079262, A105754, A251672, A251741, A251742, A251744, A251745.

LinearRecurrence[Table[1, {8}], {0, 0, 0, 0, 0, 1, 0, 0}, 43] (* Michael De Vlieger, Dec 08 2014 *)

a(n+8) = a(n)+a(n+1)+a(n+2)+a(n+3)+a(n+4)+a(n+5)+a(n+6)+a(n+7).
G.f.: x^5*(-1+x+x^2)/(-1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8) . - R. J. Mathar, Mar 28 2025
a(n) = A079262(n+2)-A079262(n+1)-A079262(n). - R. J. Mathar, Mar 28 2025

A251741 8-step Fibonacci sequence starting with 0,0,0,0,1,0,0,0.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 4, 8, 16, 31, 62, 124, 248, 495, 988, 1972, 3936, 7856, 15681, 31300, 62476, 124704, 248913, 496838, 991704, 1979472, 3951088, 7886495, 15741690, 31420904, 62717104, 125185295, 249873752, 498755800, 995532128, 1987113168

Offset: 0

Arie Bos, Dec 07 2014

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,1,1,1,1)

Other 8-step Fibonacci sequences are A079262, A105754, A251672, A251740, A251742, A251744, A251745.

LinearRecurrence[Table[1, {8}], {0, 0, 0, 0, 1, 0, 0, 0}, 43] (* Michael De Vlieger, Dec 09 2014 *)

a(n+8) = a(n)+a(n+1)+a(n+2)+a(n+3)+a(n+4)+a(n+5)+a(n+6)+a(n+7).

G.f.: x^4*(-1+x+x^2+x^3)/(-1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8) . - R. J. Mathar, Mar 28 2025

A251744 8-step Fibonacci sequence starting with 0,0,1,0,0,0,0,0.

Original entry on oeis.org

0, 0, 1, 0, 0, 0, 0, 0, 1, 2, 4, 7, 14, 28, 56, 112, 224, 447, 892, 1780, 3553, 7092, 14156, 28256, 56400, 112576, 224705, 448518, 895256, 1786959, 3566826, 7119496, 14210736, 28365072, 56617568, 113010431, 225572344, 450249432, 898711905, 1793856984

Offset: 0

Arie Bos, Dec 07 2014

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,1,1,1,1).

Other 8-step Fibonacci sequences are A079262, A105754, A251672, A251740, A251741, A251742, A251745.

LinearRecurrence[Table[1, {8}], {0, 0, 1, 0, 0, 0, 0, 0}, 43] (* Michael De Vlieger, Dec 09 2014 *)

a(n+8) = a(n)+a(n+1)+a(n+2)+a(n+3)+a(n+4)+a(n+5)+a(n+6)+a(n+7).

G.f.: x^2*(-1+x+x^2+x^3+x^4+x^5)/(-1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8) . - R. J. Mathar, Mar 28 2025

A251745 8-step Fibonacci sequence starting with 0,1,0,0,0,0,0,0.

Original entry on oeis.org

0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 3, 6, 12, 24, 48, 96, 192, 383, 764, 1525, 3044, 6076, 12128, 24208, 48320, 96448, 192513, 384262, 766999, 1530954, 3055832, 6099536, 12174864, 24301408, 48506368, 96820223, 193256184, 385745369, 769959784, 1536863736, 3067627936

Offset: 0

Arie Bos, Dec 07 2014

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,1,1,1,1)

Other 8-step Fibonacci sequences are A079262, A105754, A251672, A251740, A251741, A251742, A251744.

LinearRecurrence[Table[1, {8}], {0, 1, 0, 0, 0, 0, 0, 0}, 43] (* Michael De Vlieger, Dec 09 2014 *)

a(n+8) = a(n)+a(n+1)+a(n+2)+a(n+3)+a(n+4)+a(n+5)+a(n+6)+a(n+7).

G.f.: x*(-1+x+x^2+x^3+x^4+x^5+x^6)/(-1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8) . - R. J. Mathar, Mar 28 2025

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A251672 8-step Fibonacci sequence starting with 0,0,0,0,0,0,1,0.

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A251740 8-step Fibonacci sequence starting with 0,0,0,0,0,1,0,0.

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A251741 8-step Fibonacci sequence starting with 0,0,0,0,1,0,0,0.

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A251744 8-step Fibonacci sequence starting with 0,0,1,0,0,0,0,0.

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A251745 8-step Fibonacci sequence starting with 0,1,0,0,0,0,0,0.

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