cp's OEIS Frontend

A102424 Number of partitions of n with each part p <= 5 and each part's multiplicity m <= 5.

%I A102424 #20 Aug 24 2020 23:27:00
%S A102424 1,1,2,3,5,7,9,12,16,20,25,30,36,43,50,58,66,75,84,94,104,114,124,135,
%T A102424 145,156,165,175,184,193,201,208,214,220,224,228,230,231,231,230,228,
%U A102424 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
%N A102424 Number of partitions of n with each part p <= 5 and each part's multiplicity m <= 5.
%C A102424 There are only 76 nonzero terms.
%F A102424 a(n) = a(75 - n). - _David A. Corneth_, Aug 22 2020
%F A102424 G.f.: Product_{m=1..5} Sum_{k=0..5} x^(j*k). - _Joerg Arndt_, Aug 23 2020
%e A102424 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.
%p A102424 g:=product(sum(z^(p*m),m=0..5),p=1..5): series(g,z=0,80);
%o A102424 (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
%Y A102424 Cf. A102420 = number of partitions of integer n with exactly k = 5 parts and each part p <= 5.
%Y A102424 Cf. A000041, A102420.
%K A102424 nonn,easy,look
%O A102424 0,3
%A A102424 _Thomas Wieder_, Jan 09 2005
%E A102424 Edited by _N. J. A. Sloane_, Sep 15 2006
%E A102424 Missing term 23 inserted by _David A. Corneth_, Aug 22 2020