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A319470
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Number of partitions of n into exactly five nonzero decimal palindromes.
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4
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0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 10, 13, 18, 22, 29, 34, 42, 48, 57, 63, 72, 77, 85, 88, 95, 96, 100, 99, 101, 98, 98, 93, 92, 87, 85, 80, 79, 74, 73, 70, 69, 67, 67, 65, 66, 65, 66, 66, 67, 68, 69, 70, 72, 73, 75, 76, 78, 79, 81, 81, 83, 83, 84, 84, 85, 84
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OFFSET
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0,8
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LINKS
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FORMULA
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a(n) = [x^n y^5] 1/Product_{j>=2} (1-y*x^A002113(j)).
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MAPLE
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p:= proc(n) option remember; local i, s; s:= ""||n;
for i to iquo(length(s), 2) do if
s[i]<>s[-i] then return false fi od; true
end:
h:= proc(n) option remember; `if`(n<1, 0,
`if`(p(n), n, h(n-1)))
end:
b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(t*i<n,
0, b(n, h(i-1), t)+b(n-i, h(min(n-i, i)), t-1)))
end:
a:= n-> (k-> b(n, h(n), k)-b(n, h(n), k-1))(5):
seq(a(n), n=0..100);
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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