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
Examples
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]
Links
- 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
Programs
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Mathematica
nmax = 55; CoefficientList[Series[(x + Sum[Boole[PrimePowerQ[k] && PalindromeQ[k]] x^k, {k, 1, nmax}])^6, {x, 0, nmax}], x]
Formula
G.f.: (Sum_{k>=1} x^A084092(k))^6.
Comments