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 A282585 Number of ways to write n as an ordered sum of 3 squarefree palindromes (A071251). 2

%I

%S 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 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 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 Number of ways to write n as an ordered sum of 3 squarefree palindromes (A071251).

%C Every number can be written as the sum of 3 palindromes (see A261132 and A261422).

%C Conjecture: a(n) > 0 for any sufficiently large n.

%C Additional conjecture: every number > 3 can be written as the sum of 4 squarefree palindromes.

%H Ilya Gutkovskiy, <a href="/A282585/a282585.pdf">Extended graphical example</a>

%H Ilya Gutkovskiy, <a href="/A282585/a282585_1.pdf">Extended graphical example for additional conjecture</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PalindromicNumber.html">Palindromic Number</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Squarefree.html">Squarefree</a>

%H <a href="/index/Pac#palindromes">Index entries for sequences related to palindromes</a>

%F G.f.: (Sum_{k>=1} x^A071251(k))^3.

%e 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 nmax = 85; CoefficientList[Series[Sum[Boole[SquareFreeQ[k] && PalindromeQ[k]] x^k, {k, 1, nmax}]^3, {x, 0, nmax}], x]

%Y Cf. A002113, A005117, A035137, A071251, A091580, A091581, A260254, A261131, A261132, A261422, A280210, A282584.

%K nonn

%O 0,5

%A _Ilya Gutkovskiy_, Feb 19 2017

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Last modified October 23 05:13 EDT 2018. Contains 316519 sequences. (Running on oeis4.)