cp's OEIS Frontend

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.

%I A319439 #22 Oct 16 2018 11:24:20
%S A319439 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,
%T A319439 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,
%U A319439 12,2,15,2,13,5,14,3,17,2,13,4,15,2,17,2,12,4,15
%N 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.
%C A319439 Every number n can be written as the sum of four base-2 palindromes.
%C A319439 a(A261678(n)) = 0.
%H A319439 Rémy Sigrist, <a href="/A319439/b319439.txt">Table of n, a(n) for n = 0..10000</a>
%H A319439 A. Rajasekaran, J. Shallit, T. Smith, <a href="https://arxiv.org/abs/1706.10206">Sums of Palindromes: an Approach via Automata</a>, arXiv:1706.10206 [cs.FL], 2017.
%H A319439 Rémy Sigrist, <a href="/A319439/a319439.gp.txt">PARI program for A319439</a>
%e A319439 a(13) = 4 because 13 can be written as the sum of three base-2 palindromes in four different ways:
%e A319439 13 = 5 + 5 + 3 = 101_2  + 101_2 + 11_2,
%e A319439 13 = 7 + 3 + 3 = 111_2  +  11_2 + 11_2,
%e A319439 13 = 7 + 5 + 1 = 111_2  + 101_2 +  1_2, and
%e A319439 13 = 9 + 3 + 1 = 1001_2 +  11_2 +  1_2.
%o A319439 (PARI) See Links section.
%Y A319439 Cf. A006995, A261132, A261678.
%K A319439 nonn,base,look
%O A319439 0,4
%A A319439 _Peter Kagey_, Sep 18 2018
%E A319439 a(0) corrected by _Rémy Sigrist_, Sep 19 2018