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A102424
Number of partitions of n with each part p <= 5 and each part's multiplicity m <= 5.
0
1, 1, 2, 3, 5, 7, 9, 12, 16, 20, 25, 30, 36, 43, 50, 58, 66, 75, 84, 94, 104, 114, 124, 135, 145, 156, 165, 175, 184, 193, 201, 208, 214, 220, 224, 228, 230, 231, 231, 230, 228, 224, 220, 214, 208, 201, 193, 184, 175, 165, 156, 145, 135, 124, 114, 104, 94, 84, 75, 66, 58, 50, 43, 36, 30, 25, 20, 16, 12, 9, 7, 5, 3, 2, 1, 1
OFFSET
0,3
COMMENTS
There are only 76 nonzero terms.
FORMULA
a(n) = a(75 - n). - David A. Corneth, Aug 22 2020
G.f.: Product_{m=1..5} Sum_{k=0..5} x^(j*k). - Joerg Arndt, Aug 23 2020
EXAMPLE
a(7)=12 because we can write 7=1+1+1+1+1+2, 1+1+1+2+2, 1+2+2+2, 1+1+1+1+3, 1+1+2+3, 2+2+3, 1+3+3, 1+1+1+4, 1+2+4, 3+4, 1+1+5, 2+5. Not allowed are: 1+1+1+1+1+1+1, 16, 7.
MAPLE
g:=product(sum(z^(p*m), m=0..5), p=1..5): series(g, z=0, 80);
PROG
(PARI) nonzeroterms() = {my(res = vector(76)); forvec(x = vector(5, i, [0, 5]), c = x*[1..5]~; res[c+1]++); res} \\ David A. Corneth, Aug 22 2020
CROSSREFS
Cf. A102420 = number of partitions of integer n with exactly k = 5 parts and each part p <= 5.
Sequence in context: A126256 A347646 A062438 * A237826 A351874 A080000
KEYWORD
nonn,easy,look
AUTHOR
Thomas Wieder, Jan 09 2005
EXTENSIONS
Edited by N. J. A. Sloane, Sep 15 2006
Missing term 23 inserted by David A. Corneth, Aug 22 2020
STATUS
approved