A117760 Expansion of 1/(1 - x - x^3 - x^5 - x^7).

1, 1, 1, 2, 3, 5, 8, 13, 21, 33, 53, 85, 136, 218, 349, 559, 895, 1433, 2295, 3675, 5885, 9424, 15091, 24166, 38698, 61969, 99234, 158908, 254467, 407490, 652533, 1044932, 1673299, 2679533, 4290863, 6871162, 11003117, 17619812, 28215439, 45182718

Offset

0,4

Comments

Number of compositions of n into parts 1, 3, 5, and 7. - David Neil McGrath, Aug 18 2014

Links

Michael De Vlieger, Table of n, a(n) for n = 0..4891

Milan Janjic, Binomial Coefficients and Enumeration of Restricted Words, Journal of Integer Sequences, 2016, Vol 19, #16.7.3.

Sergey Kirgizov, Q-bonacci words and numbers, arXiv:2201.00782 [math.CO], 2022.

Index entries for linear recurrences with constant coefficients, signature (1,0,1,0,1,0,1).

Formula

a(n) = a(n-1) + a(n-3) + a(n-5) + a(n-7).

Maple

a:= proc() option remember;
  if n=0 then 1;
    elif n<=7 then combinat[fibonacci](n);
    else a(n-1) + a(n-3) + a(n-5) + a(n-7);
end if; end proc;
seq(a(n), n=0..50);  # modified by G. C. Greubel, Jul 21 2023

Mathematica

CoefficientList[Series[1/(1-x-x^3-x^5-x^7), {x, 0, 50}], x]

Prog

(PARI) Vec( 1/(1-x-x^3-x^5-x^7)+O(x^66) ) \\ Joerg Arndt, Aug 19 2014
(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1-x-x^3-x^5-x^7) )); // G. C. Greubel, Jul 21 2023
(SageMath)
@CachedFunction
def a(n): # a = A117760
    if n<8: return fibonacci(n) + int(n==0)
    else: return a(n-1) + a(n-3) + a(n-5) + a(n-7)
[a(n) for n in range(51)] # G. C. Greubel, Jul 21 2023

Crossrefs

Sequence in context: A055806 A358902 A023438 * A181600 A111917 A309676

Adjacent sequences: A117757 A117758 A117759 * A117761 A117762 A117763

Keyword

nonn,easy

Author

Roger L. Bagula, Apr 14 2006

Extensions

Edited and extended by N. J. A. Sloane, Apr 20 2006

Status

approved