A261680 Number of ordered quadruples (u,v,w,x) of binary palindromes (see A006995) with u+v+w+x=n.

1, 4, 6, 8, 13, 16, 22, 28, 34, 44, 50, 60, 59, 72, 70, 80, 92, 88, 114, 96, 125, 104, 152, 120, 172, 144, 188, 152, 215, 144, 242, 160, 272, 172, 302, 180, 329, 216, 352, 240, 388, 228, 430, 228, 442, 212, 476, 192, 506, 228, 496, 248, 540, 252, 582, 276, 592

Offset: 0

Author

N. J. A. Sloane, Sep 04 2015

Keywords

• nonn
• base

Comments

Conjecture: a(n)>0: every number is the sum of four binary palindromes. (Compare A261422, A261675.)

Links

• N. J. A. Sloane, Table of n, a(n) for n = 0..9999
• Aayush Rajasekaran, Jeffrey Shallit, and Tim Smith, Sums of Palindromes: an Approach via Nested-Word Automata, preprint arXiv:1706.10206 [cs.FL], June 30 2017.

Crossrefs

Cf. A006995, A261422, A261675, A261679.

Formula

G.f. = (Sum_{p in A006995} x^p)^4.