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

Author

Danny Rorabaugh, Nov 10 2006

Keywords

• easy
• nonn

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).

Crossrefs

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

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

Programs

Magma

R:=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

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 *)

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

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