A319439 Number of ways to write n as the sum, u + v + w, of three base-2 palindromes (from A006995) with 0 <= u <= v <= w.

1, 1, 1, 2, 1, 2, 2, 3, 2, 4, 3, 4, 2, 4, 2, 6, 2, 6, 3, 6, 2, 7, 3, 7, 3, 7, 2, 9, 2, 7, 3, 9, 3, 10, 4, 10, 4, 11, 3, 12, 2, 11, 3, 11, 1, 12, 2, 10, 4, 11, 2, 14, 3, 11, 4, 13, 1, 13, 2, 11, 3, 12, 2, 15, 2, 13, 5, 14, 3, 17, 2, 13, 4, 15, 2, 17, 2, 12, 4, 15

Offset: 0

Author

Peter Kagey, Sep 18 2018

Keywords

• nonn
• base
• look

Comments

Every number n can be written as the sum of four base-2 palindromes.

a(A261678(n)) = 0.

Examples

			a(13) = 4 because 13 can be written as the sum of three base-2 palindromes in four different ways:
13 = 5 + 5 + 3 = 101_2  + 101_2 + 11_2,
13 = 7 + 3 + 3 = 111_2  +  11_2 + 11_2,
13 = 7 + 5 + 1 = 111_2  + 101_2 +  1_2, and
13 = 9 + 3 + 1 = 1001_2 +  11_2 +  1_2.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000
• A. Rajasekaran, J. Shallit, T. Smith, Sums of Palindromes: an Approach via Automata, arXiv:1706.10206 [cs.FL], 2017.
• Rémy Sigrist, PARI program for A319439

Crossrefs

Cf. A006995, A261132, A261678.

Programs

PARI

See Links section.

Extensions

a(0) corrected by Rémy Sigrist, Sep 19 2018