|
|
A029016
|
|
Expansion of 1/((1-x)(1-x^2)(1-x^5)(1-x^12)).
|
|
1
|
|
|
1, 1, 2, 2, 3, 4, 5, 6, 7, 8, 10, 11, 14, 15, 18, 20, 23, 26, 29, 32, 36, 39, 44, 47, 53, 57, 63, 68, 74, 80, 87, 93, 101, 107, 116, 123, 133, 141, 151, 160, 171, 181, 193, 203, 216, 227, 241, 253, 268, 281, 297, 311
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Number of partitions of n into parts 1, 2, 5, and 12. - Joerg Arndt, May 20 2014
|
|
LINKS
|
Index entries for linear recurrences with constant coefficients, signature (1, 1, -1, 0, 1, -1, -1, 1, 0, 0, 0, 1, -1, -1, 1, 0, -1, 1, 1, -1).
|
|
MAPLE
|
M := Matrix(20, (i, j)-> if (i=j-1) or (j=1 and member(i, [1, 2, 5, 8, 12, 15, 18, 19])) then 1 elif j=1 and member(i, [3, 6, 7, 13, 14, 17, 20]) then -1 else 0 fi); a := n -> (M^(n))[1, 1]; seq (a(n), n=0..51); # Alois P. Heinz, Jul 25 2008
|
|
MATHEMATICA
|
s = 1/((1-x)(1-x^2)(1-x^5)(1-x^12)) + O[x]^100; CoefficientList[s, x] (* Jean-François Alcover, Nov 05 2015 *)
LinearRecurrence[{1, 1, -1, 0, 1, -1, -1, 1, 0, 0, 0, 1, -1, -1, 1, 0, -1, 1, 1, -1}, {1, 1, 2, 2, 3, 4, 5, 6, 7, 8, 10, 11, 14, 15, 18, 20, 23, 26, 29, 32}, 80] (* Harvey P. Dale, Jun 22 2017 *)
|
|
PROG
|
(PARI) a(n)=floor((2*n^3+60*n^2+513*n+1773)/1440+(n+1)*(-1)^n/96+[0, -1, 0, 1, 0, 2][n%6+1]*(-1)^(n\6)/6) \\ Tani Akinari, May 19 2014
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|