This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A282585 #12 Feb 16 2025 08:33:41
%S A282585 0,0,0,1,3,6,7,9,12,19,21,21,18,24,27,28,18,18,19,24,15,10,6,12,12,12,
%T A282585 9,9,12,15,18,12,9,7,15,15,15,9,12,15,18,18,12,9,9,18,15,12,0,9,9,9,0,
%U A282585 0,0,6,6,9,12,9,12,15,18,18,12,9,13,18,18,18,9,15,18,21,18,12,9,15,21,21,21,9,18,21,24,18
%N A282585 Number of ways to write n as an ordered sum of 3 squarefree palindromes (A071251).
%C A282585 Every number can be written as the sum of 3 palindromes (see A261132 and A261422).
%C A282585 Conjecture: a(n) > 0 for any sufficiently large n.
%C A282585 Additional conjecture: every number > 3 can be written as the sum of 4 squarefree palindromes.
%H A282585 Ilya Gutkovskiy, <a href="/A282585/a282585.pdf">Extended graphical example</a>
%H A282585 Ilya Gutkovskiy, <a href="/A282585/a282585_1.pdf">Extended graphical example for additional conjecture</a>
%H A282585 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PalindromicNumber.html">Palindromic Number</a>
%H A282585 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Squarefree.html">Squarefree</a>
%H A282585 <a href="/index/Pac#palindromes">Index entries for sequences related to palindromes</a>
%F A282585 G.f.: (Sum_{k>=1} x^A071251(k))^3.
%e A282585 a(22) = 6 because we have [11, 6, 5], [11, 5, 6] [6, 11, 5], [6, 5, 11], [5, 11, 6] and [5, 6, 11].
%t A282585 nmax = 85; CoefficientList[Series[Sum[Boole[SquareFreeQ[k] && PalindromeQ[k]] x^k, {k, 1, nmax}]^3, {x, 0, nmax}], x]
%Y A282585 Cf. A002113, A005117, A035137, A071251, A091580, A091581, A260254, A261131, A261132, A261422, A280210, A282584.
%K A282585 nonn,base
%O A282585 0,5
%A A282585 _Ilya Gutkovskiy_, Feb 19 2017