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

Author

Ilya Gutkovskiy, Feb 19 2017

Keywords

• nonn
• base

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.

Examples

			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].
		

Links

• 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

Crossrefs

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

Programs

Mathematica

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

Formula

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