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A282585
Number of ways to write n as an ordered sum of 3 squarefree palindromes (A071251).
2
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
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]
KEYWORD
nonn,base
AUTHOR
Ilya Gutkovskiy, Feb 19 2017
STATUS
approved