A123526 Octanacci numbers.

1, 1, 1, 1, 1, 1, 1, 1, 8, 15, 29, 57, 113, 225, 449, 897, 1793, 3578, 7141, 14253, 28449, 56785, 113345, 226241, 451585, 901377, 1799176, 3591211, 7168169, 14307889, 28558993, 57004641, 113783041, 227114497, 453327617, 904856058, 1806120905

Offset

1,9

Links

Robert Price, Table of n, a(n) for n = 1..1000

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

Formula

a(n)=1 for 1 <= n <= 8, a(n) = a(n-1) + a(n-2) +...+ a(n-8) for n > 8.

G.f.: x*(1 -x^2 -2*x^3 -3*x^4 -4*x^5 -5*x^6 -6*x^7)/(1 -x -x^2 -x^3 -x^4 -x^5 -x^6 -x^7 -x^8). - Colin Barker, Oct 19 2015

Maple

m:=50; S:=series( x*(1-x^2-2*x^3-3*x^4-4*x^5-5*x^6-6*x^7)/(1-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8), x, m+1):
seq(coeff(S, x, j), j=1..m); # G. C. Greubel, Mar 10 2021

Mathematica

Module[{nn=8, lr}, lr=PadRight[{}, nn, 1]; LinearRecurrence[lr, lr, 20]] (* Harvey P. Dale, Feb 04 2015 *)

Prog

(PARI) Vec(x*(1-x^2-2*x^3-3*x^4-4*x^5-5*x^6-6*x^7)/(1-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8) + O(x^50)) \\ Colin Barker, Oct 19 2015
(Sage)
@CachedFunction
def A123526(n):
    if (n<9): return 1
    else: return sum(A(n-j) for j in (1..8))
[A123526(n) for n in [1..50]] # G. C. Greubel, Mar 10 2021
(Magma)
R<x>:=PowerSeriesRing(Integers(), 50);
Coefficients(R!( x*(1-x^2-2*x^3-3*x^4-4*x^5-5*x^6-6*x^7)/(1-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8) )); // G. C. Greubel, Mar 10 2021

Crossrefs

Cf. A000045, A000213, A000288, A000322, A000383, A060455, A079262.

Cf. A254412, A254413. Indices of primes and primes in this sequence.

Sequence in context: A240522 A132298 A188558 * A083686 A293360 A371388

Adjacent sequences: A123523 A123524 A123525 * A123527 A123528 A123529

Keyword

easy,nonn

Author

Danny Rorabaugh, Nov 10 2006

Status

approved