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%I #30 Jul 21 2023 17:22:15
%S 1,1,1,2,3,5,8,13,21,33,53,85,136,218,349,559,895,1433,2295,3675,5885,
%T 9424,15091,24166,38698,61969,99234,158908,254467,407490,652533,
%U 1044932,1673299,2679533,4290863,6871162,11003117,17619812,28215439,45182718
%N Expansion of 1/(1 - x - x^3 - x^5 - x^7).
%C Number of compositions of n into parts 1, 3, 5, and 7. - _David Neil McGrath_, Aug 18 2014
%H Michael De Vlieger, <a href="/A117760/b117760.txt">Table of n, a(n) for n = 0..4891</a>
%H Milan Janjic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Janjic/janjic73.html">Binomial Coefficients and Enumeration of Restricted Words</a>, Journal of Integer Sequences, 2016, Vol 19, #16.7.3.
%H Sergey Kirgizov, <a href="https://arxiv.org/abs/2201.00782">Q-bonacci words and numbers</a>, arXiv:2201.00782 [math.CO], 2022.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,0,1,0,1).
%F a(n) = a(n-1) + a(n-3) + a(n-5) + a(n-7).
%p a:= proc() option remember;
%p if n=0 then 1;
%p elif n<=7 then combinat[fibonacci](n);
%p else a(n-1) + a(n-3) + a(n-5) + a(n-7);
%p end if; end proc;
%p seq(a(n), n=0..50); # modified by _G. C. Greubel_, Jul 21 2023
%t CoefficientList[Series[1/(1-x-x^3-x^5-x^7), {x,0,50}], x]
%o (PARI) Vec( 1/(1-x-x^3-x^5-x^7)+O(x^66) ) \\ _Joerg Arndt_, Aug 19 2014
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1-x-x^3-x^5-x^7) )); // _G. C. Greubel_, Jul 21 2023
%o (SageMath)
%o @CachedFunction
%o def a(n): # a = A117760
%o if n<8: return fibonacci(n) + int(n==0)
%o else: return a(n-1) + a(n-3) + a(n-5) + a(n-7)
%o [a(n) for n in range(51)] # _G. C. Greubel_, Jul 21 2023
%K nonn,easy
%O 0,4
%A _Roger L. Bagula_, Apr 14 2006
%E Edited and extended by _N. J. A. Sloane_, Apr 20 2006
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