A102424 Number of partitions of n with each part p <= 5 and each part's multiplicity m <= 5.
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
Examples
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.
Crossrefs
Programs
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Maple
g:=product(sum(z^(p*m),m=0..5),p=1..5): series(g,z=0,80);
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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
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
Extensions
Edited by N. J. A. Sloane, Sep 15 2006
Missing term 23 inserted by David A. Corneth, Aug 22 2020
Comments