Number of palindromic (in base 7) triples that sum to n.

1, 1, 2, 3, 4, 5, 7, 7, 9, 9, 10, 9, 10, 8, 8, 6, 7, 5, 6, 4, 5, 4, 5, 3, 6, 4, 5, 4, 5, 4, 5, 3, 7, 5, 6, 5, 6, 5, 6, 3, 8, 5, 6, 5, 6, 5, 6, 3, 10, 6, 8, 7, 9, 8, 10, 6, 14, 9, 10, 9, 9, 8, 8, 5, 13, 8, 10, 9, 9, 9, 9, 6, 14, 9, 10, 9, 9, 9, 9, 7, 16, 10, 12

0

Three terms seem to be enough.

T. D. Noe, Plot of 10000 terms

T. D. Noe, Table of 10000 terms

Javier Cilleruelo and Florian Luca, Every positive integer is a sum of three palindromes, arXiv 1602.06208 (Feb 19 2016)

Yu Gao, Represent a natural number as the sum of palindromes in various bases, arXiv 1508.06185 (Aug 24 2015)

(Mma) base = 7; mx = 100; pal = Select[Range[0, mx], (d = IntegerDigits[#, base]; d == Reverse[d]) &]; Table[Length[IntegerPartitions[n, {3}, pal]], {n, 0, mx}]

nonn,base

T. D. Noe, Sep 23 2015