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 A308775 Sum of all the parts in the partitions of n into 4 parts. 4
 0, 0, 0, 0, 4, 5, 12, 21, 40, 54, 90, 121, 180, 234, 322, 405, 544, 663, 846, 1026, 1280, 1512, 1848, 2162, 2592, 3000, 3536, 4050, 4732, 5365, 6180, 6975, 7968, 8910, 10098, 11235, 12636, 13986, 15618, 17199, 19120, 20951, 23142, 25284, 27808, 30240, 33120 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Table of n, a(n) for n=0..46. Index entries for sequences related to partitions FORMULA a(n) = n * A026810(n). a(n) = A308733(n) + A308758(n) + A308759(n) + A308760(n). Conjectures from Colin Barker, Jun 24 2019: (Start) G.f.: x^4*(4 + 5*x + 8*x^2 + 8*x^3 + 10*x^4 + 7*x^5 + 6*x^6) / ((1 - x)^5*(1 + x)^3*(1 + x^2)^2*(1 + x + x^2)^2). a(n) = a(n-2) + 2*a(n-3) + 2*a(n-4) - 2*a(n-5) - 3*a(n-6) - 4*a(n-7) + 4*a(n-9) + 3*a(n-10) + 2*a(n-11) - 2*a(n-12) - 2*a(n-13) - a(n-14) + a(n-16) for n>15. (End) EXAMPLE Figure 1: The partitions of n into 4 parts for n = 8, 9, .. 1+1+1+9 1+1+2+8 1+1+3+7 1+1+4+6 1+1+1+8 1+1+5+5 1+1+2+7 1+2+2+7 1+1+1+7 1+1+3+6 1+2+3+6 1+1+2+6 1+1+4+5 1+2+4+5 1+1+3+5 1+2+2+6 1+3+3+5 1+1+1+6 1+1+4+4 1+2+3+5 1+3+4+4 1+1+1+5 1+1+2+5 1+2+2+5 1+2+4+4 2+2+2+6 1+1+2+4 1+1+3+4 1+2+3+4 1+3+3+4 2+2+3+5 1+1+3+3 1+2+2+4 1+3+3+3 2+2+2+5 2+2+4+4 1+2+2+3 1+2+3+3 2+2+2+4 2+2+3+4 2+3+3+4 2+2+2+2 2+2+2+3 2+2+3+3 2+3+3+3 3+3+3+3 -------------------------------------------------------------------------- n | 8 9 10 11 12 ... -------------------------------------------------------------------------- a(n) | 40 54 90 121 180 ... -------------------------------------------------------------------------- - Wesley Ivan Hurt, Sep 07 2019 MATHEMATICA Table[n*Sum[Sum[Sum[1, {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 100}] CROSSREFS Cf. A026810, A308733, A308758, A308759, A308760. Sequence in context: A309479 A352720 A369697 * A305335 A123102 A274077 Adjacent sequences: A308772 A308773 A308774 * A308776 A308777 A308778 KEYWORD nonn AUTHOR Wesley Ivan Hurt, Jun 23 2019 STATUS approved

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Last modified August 11 01:05 EDT 2024. Contains 375059 sequences. (Running on oeis4.)