This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A102422 #8 Mar 31 2012 14:40:21 %S A102422 1,1,2,3,5,7,9,11,14,16,18,19,20,20,19,18,16,14,11,9,7,5,3,2,1,1,0,0, %T A102422 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, %U A102422 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 %N A102422 Number of partitions of n with k <= 5 parts and each part p <= 5. %C A102422 There are only 26 nonzero terms. %C A102422 Contribution from _Toby Gottfried_, Feb 19 2009: (Start) %C A102422 a(n) is the number of partitions of n+5 into exactly 5 parts with each part p: 1 <= p <= 6 %C A102422 i.e. the number of different ways to get a total of n+5 with 5 (normal, 6-sided) dice in any order (End) %F A102422 G.f.: = 1+z+2*z^2+3*z^3+5*z^4+7*z^5+9*z^6+11*z^7+14*z^8+16*z^9+18*z^10+19*z^11+20*z^12+20*z^13+19*z^14+18*z^15+16*z^16+14*z^17+11*z^18+9*z^19 +7*z^20+5*z^21+3*z^22+2*z^23+z^24+z^25. %e A102422 a(7)=11 because we can write 7=1+2+2+2 or 5+2 or 1+2+4 or 3+4 or 1+3+3 or 1+1+1+1+3 or 1+1+2+3 or 2+2+3 or 1+1+1+2+2 1+1+1+4 or 1+1+5. %e A102422 A total of 8 comes from 1+1+1+1+4, 1+1+1+2+3, 1+1+2+2+2 and a(3) = 3 [8 = 3+5] [From _Toby Gottfried_, Feb 19 2009] %Y A102422 See A102420 for k=5 and p<=5. %Y A102422 Cf. A000041, A102420, A063746. %Y A102422 Contribution from _Toby Gottfried_, Feb 19 2009: (Start) %Y A102422 A102420 has the numbers for 4 dice %Y A102422 A063260 gives the number of permuted rolls of each possible total for any number of dice. (End) %K A102422 easy,nonn %O A102422 0,3 %A A102422 _Thomas Wieder_, Jan 09 2005