cp's OEIS Frontend

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.

A308822 Sum of all the parts in the partitions of n into 5 parts.

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%I A308822 #11 Sep 09 2019 01:41:55
%S A308822 0,0,0,0,0,5,6,14,24,45,70,110,156,234,322,450,592,799,1026,1330,1680,
%T A308822 2121,2618,3243,3936,4800,5746,6885,8148,9657,11310,13237,15360,17820,
%U A308822 20502,23590,26928,30747,34884,39546,44600,50266,56364,63167,70488,78615
%N A308822 Sum of all the parts in the partitions of n into 5 parts.
%H A308822 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308822 a(n) = n * A026811(n).
%F A308822 a(n) = A308823(n) + A308824(n) + A308825(n) + A308826(n) + A308827(n).
%e A308822 The partitions of n into 5 parts for n = 10, 11, ..
%e A308822                                                        1+1+1+1+10
%e A308822                                                         1+1+1+2+9
%e A308822                                                         1+1+1+3+8
%e A308822                                                         1+1+1+4+7
%e A308822                                                         1+1+1+5+6
%e A308822                                             1+1+1+1+9   1+1+2+2+8
%e A308822                                             1+1+1+2+8   1+1+2+3+7
%e A308822                                             1+1+1+3+7   1+1+2+4+6
%e A308822                                             1+1+1+4+6   1+1+2+5+5
%e A308822                                             1+1+1+5+5   1+1+3+3+6
%e A308822                                 1+1+1+1+8   1+1+2+2+7   1+1+3+4+5
%e A308822                                 1+1+1+2+7   1+1+2+3+6   1+1+4+4+4
%e A308822                                 1+1+1+3+6   1+1+2+4+5   1+2+2+2+7
%e A308822                     1+1+1+1+7   1+1+1+4+5   1+1+3+3+5   1+2+2+3+6
%e A308822                     1+1+1+2+6   1+1+2+2+6   1+1+3+4+4   1+2+2+4+5
%e A308822                     1+1+1+3+5   1+1+2+3+5   1+2+2+2+6   1+2+3+3+5
%e A308822         1+1+1+1+6   1+1+1+4+4   1+1+2+4+4   1+2+2+3+5   1+2+3+4+4
%e A308822         1+1+1+2+5   1+1+2+2+5   1+1+3+3+4   1+2+2+4+4   1+3+3+3+4
%e A308822         1+1+1+3+4   1+1+2+3+4   1+2+2+2+5   1+2+3+3+4   2+2+2+2+6
%e A308822         1+1+2+2+4   1+1+3+3+3   1+2+2+3+4   1+3+3+3+3   2+2+2+3+5
%e A308822         1+1+2+3+3   1+2+2+2+4   1+2+3+3+3   2+2+2+2+5   2+2+2+4+4
%e A308822         1+2+2+2+3   1+2+2+3+3   2+2+2+2+4   2+2+2+3+4   2+2+3+3+4
%e A308822         2+2+2+2+2   2+2+2+2+3   2+2+2+3+3   2+2+3+3+3   2+3+3+3+3
%e A308822 --------------------------------------------------------------------------
%e A308822   n  |     10          11          12          13          14        ...
%e A308822 --------------------------------------------------------------------------
%e A308822 a(n) |     70         110         156         234         322        ...
%e A308822 --------------------------------------------------------------------------
%e A308822 - _Wesley Ivan Hurt_, Sep 08 2019
%t A308822 Table[n*Sum[Sum[Sum[Sum[1, {i, j, Floor[(n - j - k - l)/2]}], {j, k, Floor[(n - k - l)/3]}], {k, l, Floor[(n - l)/4]}], {l, Floor[n/5]}], {n, 0, 100}]
%Y A308822 Cf. A026811, A308823, A308824, A308825, A308826, A308827.
%K A308822 nonn
%O A308822 0,6
%A A308822 _Wesley Ivan Hurt_, Jun 26 2019