OFFSET
0,2
COMMENTS
Number of partitions of n into two kinds of part 1 and one kind of parts 2, 5, and 10. - Joerg Arndt, May 10 2014
REFERENCES
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 152.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Christian G. Bower, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1,1,-2,0,2,-1,1,-2,0,2,-1,-1,2,0,-2,1).
FORMULA
G.f.: 1 / ( ( 1 - x )^2 * ( 1 - x^2 ) * ( 1 - x^5 ) * ( 1 - x^10 ) ).
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) + a(n-5) - 2*a(n-6) + 2*a(n-8) - a(n-9) + a(n-10) - 2*a(n-11) + 2*a(n-13) - a(n-14) - a(n-15) + 2*a(n-16) - 2*a(n-18) + a(n-19). - Fung Lam, May 07 2014
a(n) ~ n^4 / 2400 as n->oo. - Daniel Checa, Jul 11 2023
MAPLE
1/(1-x)^2/(1-x^2)/(1-x^5)/(1-x^10)
a:= proc(n) local m, r; m := iquo(n, 10, 'r'); r:= r+1; (55+(119+(95+ 25*m) *m) *m) *m/6+ [1, 2, 4, 6, 9, 13, 18, 24, 31, 39][r]+ [0, 26, 61, 99, 146, 202, 267, 341, 424, 516][r]*m/6+ [0, 10, 21, 33, 46, 60, 75, 91, 108, 126][r]*m^2/2+ (5*r-5) *m^3/3 end: seq(a(n), n=0..100); # Alois P. Heinz, Oct 05 2008
MATHEMATICA
CoefficientList[Series[1/((1-x)^2(1-x^2)(1-x^5)(1-x^10)), {x, 0, 100}], x] (* Vladimir Joseph Stephan Orlovsky, Jan 25 2012 *)
PROG
(PARI) a(n)=if(n<0, 0, polcoeff(1/((1-x)^2*(1-x^2)*(1-x^5)*(1-x^10))+x*O(x^n), n))
(PARI) a(n)=floor((n^4+38*n^3+476*n^2+2185*n+3735)/2400+(n+1)*(-1)^n/160+(n\5+1)*[0, 0, 1, 0, -1][n%5+1]/10) \\ Tani Akinari, May 10 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Corrected and extended by Simon Plouffe
STATUS
approved