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
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
Programs
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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
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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
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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
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