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

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, 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, 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

Offset

0,5

Comments

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

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

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

Links

Table of n, a(n) for n=0..85.

Ilya Gutkovskiy, Extended graphical example

Ilya Gutkovskiy, Extended graphical example for additional conjecture

Eric Weisstein's World of Mathematics, Palindromic Number

Eric Weisstein's World of Mathematics, Squarefree

Index entries for sequences related to palindromes

Formula

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

Example

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].

Mathematica

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

Crossrefs

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

Sequence in context: A087916 A359263 A296693 * A280210 A023982 A189092

Adjacent sequences: A282582 A282583 A282584 * A282586 A282587 A282588

Keyword

nonn,base

Author

Ilya Gutkovskiy, Feb 19 2017

Status

approved