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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, 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
0,4
COMMENTS
Every number n can be written as the sum of four base-2 palindromes.
a(A261678(n)) = 0.
LINKS
A. Rajasekaran, J. Shallit, T. Smith, Sums of Palindromes: an Approach via Automata, arXiv:1706.10206 [cs.FL], 2017.
EXAMPLE
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.
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn,base,look
AUTHOR
Peter Kagey, Sep 18 2018
EXTENSIONS
a(0) corrected by Rémy Sigrist, Sep 19 2018
STATUS
approved