OFFSET
0,3
COMMENTS
Number of partitions of n into parts 1, 2, 4 and 8. - Ilya Gutkovskiy, May 24 2017
REFERENCES
D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 105.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 233
Index entries for linear recurrences with constant coefficients, signature (1,1,-1,1,-1,-1,1,1,-1,-1,1,-1,1,1,-1).
FORMULA
G.f.: 1/((1-x)*(1-x^2)*(1-x^4)*(1-x^8)).
a(n) = floor(((n+14)*(3*(n+1)*(-1)^n + 2*n^2 + 17*n + 57) + 24*(floor(n/2) + 1)*(-1)^floor(n/2))/768). - Tani Akinari, Jun 16 2013
a(n) ~ 1/384*n^3. - Ralf Stephan, Apr 29 2014
MAPLE
a:= proc(n) local m, r; m := iquo(n, 8, 'r'); r:= iquo(r, 2)+1; ([11, 17, 26, 35][r]+ (9+ 3*r+ 4*m) *m) *m/3+ [1, 2, 4, 6][r] end: seq(a(n), n=0..100); # Alois P. Heinz, Oct 06 2008
MATHEMATICA
CoefficientList[1/((1-x)*(1-x^2)*(1-x^4)*(1-x^8)) + O[x]^65, x] (* Jean-François Alcover, May 29 2015 *)
LinearRecurrence[{1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1}, {1, 1, 2, 2, 4, 4, 6, 6, 10, 10, 14, 14, 20, 20, 26}, 65] (* Ray Chandler, Jul 15 2015 *)
PROG
(PARI) my(x='x+O('x^65)); Vec(1/((1-x)*(1-x^2)*(1-x^4)*(1-x^8))) \\ G. C. Greubel, Feb 01 2020
(Magma) R<x>:=PowerSeriesRing(Integers(), 65); Coefficients(R!( (&*[1/(1-x^(2^j)): j in [0..3]]) )); // G. C. Greubel, Feb 01 2020
(Sage)
def A077952_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/((1-x)*(1-x^2)*(1-x^4)*(1-x^8)) ).list()
A077952_list(65) # G. C. Greubel, Feb 01 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved