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A123526
Octanacci numbers.
10
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
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. A254412, A254413. Indices of primes and primes in this sequence.
Sequence in context: A240522 A132298 A188558 * A083686 A293360 A371388
KEYWORD
easy,nonn
AUTHOR
Danny Rorabaugh, Nov 10 2006
STATUS
approved