|
Search: id:A089958
|
|
|
| A089958 |
|
Number of partitions of n in which every part occurs 2, 3, or 5 times. |
|
+0
2
|
|
| 1, 0, 1, 1, 1, 1, 3, 1, 3, 4, 4, 4, 8, 5, 9, 11, 11, 12, 20, 15, 23, 27, 28, 31, 45, 38, 52, 61, 64, 71, 96, 87, 112, 129, 136, 151, 194, 184, 227, 259, 275, 304, 376, 368, 441, 499, 531, 586, 704, 705, 826, 927, 989, 1088, 1280, 1302, 1500, 1672, 1787, 1960, 2267
(list; graph; listen)
|
|
|
OFFSET
|
0,7
|
|
|
COMMENT
|
Also number of partitions of n in which every part is congruent to {2, 3, 6, 9, 10} mod 12. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 07 2005
|
|
REFERENCES
|
M. V. Subbarao, Combinatorial proofs of some identities, Proc. Washington State Univ. Conf. Number Theory, 1971, pp. 80-91.
M. V. Subbarao, On a partition theorem of Mac Mahon-Andrews, Proc. Amer. Math. Soc., 27, 1971, 449-450.
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Partition Function P
|
|
FORMULA
|
Euler transform of period 12 sequence [0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, ...]. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 07 2005
Expansion of q^(-5/24)eta(q^6)eta(q^4)/(eta(q^2)eta(q^3)) in powers of q.
G.f.=product(1+x^(2j)+x^(3j)+x^(5j), j=1..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 05 2006
|
|
EXAMPLE
|
a(11)=4 because we have [4,4,1,1,1],[3,3,3,1,1],[3,3,1,1,1,1,1] and [2,2,2,1,1,1,1,1].
|
|
MAPLE
|
g:=product(1+x^(2*j)+x^(3*j)+x^(5*j), j=1..50): gser:=series(g, x=0, 63): seq(coeff(gser, x, n), n=0..60); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 05 2006
|
|
PROGRAM
|
(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^4+A)*eta(x^6+A)/eta(x^2+A)/eta(x^3+A), n))} /* Michael Somos Jan 19 2005 */
|
|
CROSSREFS
|
Sequence in context: A081772 A050121 A029152 this_sequence A162932 A008924 A021323
Adjacent sequences: A089955 A089956 A089957 this_sequence A089959 A089960 A089961
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Eric Weisstein (eric(AT)weisstein.com), Nov 16, 2003
|
|
|
Search completed in 0.005 seconds
|
