A282845 Number of ways to write n as an ordered sum of 6 prime power palindromes (A084092).

0, 0, 0, 0, 0, 0, 1, 6, 21, 56, 126, 246, 432, 702, 1077, 1576, 2232, 3072, 4112, 5352, 6801, 8422, 10197, 12102, 14117, 16146, 18177, 20112, 21882, 23382, 24661, 25566, 26136, 26316, 26181, 25560, 24677, 23436, 21981, 20226, 18486, 16536, 14642, 12702, 10962, 9166, 7662, 6222, 5042, 3912, 3096, 2306, 1746, 1236, 921, 600

Offset

0,8

Comments

Is there k which satisfies a(n) > 0 for all n > k?

Links

Table of n, a(n) for n=0..55.

Ilya Gutkovskiy, Extended graphical example

Eric Weisstein's World of Mathematics, Prime Power

Eric Weisstein's World of Mathematics, Palindromic Number

Index entries for sequences related to palindromes

Formula

G.f.: (Sum_{k>=1} x^A084092(k))^6.

Example

a(7) = 6 because we have:
[2, 1, 1, 1, 1, 1]
[1, 2, 1, 1, 1, 1]
[1, 1, 2, 1, 1, 1]
[1, 1, 1, 2, 1, 1]
[1, 1, 1, 1, 2, 1]
[1, 1, 1, 1, 1, 2]

Mathematica

nmax = 55; CoefficientList[Series[(x + Sum[Boole[PrimePowerQ[k] && PalindromeQ[k]] x^k, {k, 1, nmax}])^6, {x, 0, nmax}], x]

Crossrefs

Cf. A000961, A002113, A002385, A084092, A260254, A261131, A261132, A261422, A282585.

Sequence in context: A132366 A015641 A292950 * A341135 A050190 A008498

Adjacent sequences: A282842 A282843 A282844 * A282846 A282847 A282848

Keyword

base,nonn

Author

Ilya Gutkovskiy, Feb 22 2017

Status

approved