A327792 a(n) is the greatest nonnegative number which has a partition into a triangular number (A000217), a square number (A000290), and a pentagonal number (A000326) in n different ways.

0, 18, 168, 78, 243, 130, 553, 455, 515, 658, 865, 945, 633, 1918, 2258, 1385, 1583, 2828, 2135, 2335, 2785, 4533, 3168, 3478, 2790, 3868, 4193, 7328, 4953, 5278, 6390, 8148, 8015, 4585, 9160, 10485, 7613, 12333, 12025, 10178, 9923, 9720, 12558, 11340, 17420, 11753, 14893, 16155, 16415, 14343, 18053, 19803, 16608, 27283

Offset

1,2

Comments

The largest nonnegative number k such that A240088(k) = n.

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..200

Example

a(0) does not exist since all numbers can be represented as the sum of a triangular, square & pentagonal number.

Mathematica

f[n_] := Block[{j, k = 1, lenq, lenr, v = {}, t = PolygonalNumber[3, Range[0, 1 + Sqrt[2 n]]], s = PolygonalNumber[4, Range[0, 1 + Sqrt[n]]], p = PolygonalNumber[5, Range[0, 2 + Sqrt[2 n/3]]]}, u = Select[Union[Join[t, s, p]], # < n + 1 &]; q = IntegerPartitions[n, {3}, u]; lenq = 1 + Length@q; While[k < lenq, j = 1; r = q[[k]]; rr = Permutations@r; lenr = 1 + Length@rr; While[j < lenr, If[ MemberQ[t, rr[[j, 1]]] && MemberQ[s, rr[[j, 2]]] && MemberQ[p, rr[[j, 3]]], AppendTo[v, rr[[j]]]]; j++]; k++]; Length@v];

Crossrefs

Cf. A000217, A000290, A000326, A240088, A275999, A327793.

Sequence in context: A041618 A055915 A208827 * A071539 A125381 A126539

Adjacent sequences: A327789 A327790 A327791 * A327793 A327794 A327795

Keyword

nonn

Author

Robert G. Wilson v, Sep 25 2019

Status

approved