A251672 -id:A251672 - cp's OEIS frontend

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

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

A251742 8-step Fibonacci sequence starting with 0,0,0,1,0,0,0,0.

Original entry on oeis.org

0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 4, 8, 15, 30, 60, 120, 240, 479, 956, 1908, 3808, 7601, 15172, 30284, 60448, 120656, 240833, 480710, 959512, 1915216, 3822831, 7630490, 15230696, 30400944, 60681232, 121121631, 241762552, 482565592, 963215968, 1922609105

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, A251744, A251745.

LinearRecurrence[Table[1, {8}], {0, 0, 0, 1, 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^3*(-1+x+x^2+x^3+x^4)/(-1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8) . - R. J. Mathar, Mar 28 2025
a(n) = A172318(n-3)-2*A172318(n-4)+A172318(n-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

A251654 4-step Fibonacci sequence starting with 0, 1, 1, 0.

Original entry on oeis.org

0, 1, 1, 0, 2, 4, 7, 13, 26, 50, 96, 185, 357, 688, 1326, 2556, 4927, 9497, 18306, 35286, 68016, 131105, 252713, 487120, 938954, 1809892, 3488679, 6724645, 12962170, 24985386, 48160880, 92833081, 178941517, 344920864, 664856342, 1281551804

Offset: 0

Arie Bos, Dec 06 2014

Index entries for linear recurrences with constant coefficients, signature (1,1,1,1).

Other 4-step Fibonacci sequences are A000078, A000288, A001630, A001631, A001648, A073817, A100532, A251655, A251656, A251672, A251703, A251704, A251705.

NB. see A251655 for the program and apply it to 0,1,1,0.

LinearRecurrence[Table[1, {4}], {0, 1, 1, 0}, 36] (* Michael De Vlieger, Dec 09 2014 *)

a(n+4) = a(n) + a(n+1) + a(n+2) + a(n+3).
G.f.: x*(-1+2*x^2)/(-1+x+x^2+x^3+x^4). - R. J. Mathar, Mar 28 2025
a(n) = A000078(n+2)-2*A000078(n). - R. J. Mathar, Mar 28 2025

A251655 4-step Fibonacci sequence starting with 0, 1, 1, 1.

Original entry on oeis.org

0, 1, 1, 1, 3, 6, 11, 21, 41, 79, 152, 293, 565, 1089, 2099, 4046, 7799, 15033, 28977, 55855, 107664, 207529, 400025, 771073, 1486291, 2864918, 5522307, 10644589, 20518105, 39549919, 76234920, 146947533, 283250477, 545982849, 1052415779, 2028596638

Offset: 0

Arie Bos, Dec 06 2014

Tamás Lengyel and Diego Marques, The 2-adic Order of Some Generalized Fibonacci Numbers, INTEGERS, 17, 2017, A5.
Index entries for linear recurrences with constant coefficients, signature (1,1,1,1).

Other 4-step Fibonacci sequences are A000078, A000288, A001630, A001631, A001648, A073817, A100532, A251654, A251656, A251672, A251703, A251704, A251705.

(see www.jsoftware.com) First construct the generating matrix
   [M=: (#.@}: + {:)\"1&.|: <:/~i.4
1 1 1 1
1 2 2 2
2 3 4 4
4 6 7 8
Given that matrix, one can produce the first 4*250 numbers with
, M(+/ . *)^:(i.250) 0 1 1 1x

LinearRecurrence[Table[1, {4}], {0, 1, 1, 1}, 36] (* Michael De Vlieger, Dec 09 2014 *)

a(n+4) = a(n) + a(n+1) + a(n+2) + a(n+3).
G.f.: x*(x-1)*(1+x)/(-1+x+x^2+x^3+x^4) . - R. J. Mathar, Mar 28 2025
a(n) = A000078(n+2)-A000078(n). - R. J. Mathar, Mar 28 2025

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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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A251742 8-step Fibonacci sequence starting with 0,0,0,1,0,0,0,0.

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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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A251654 4-step Fibonacci sequence starting with 0, 1, 1, 0.

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A251655 4-step Fibonacci sequence starting with 0, 1, 1, 1.

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