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A319454
Number of partitions of 2n into exactly n nonzero decimal palindromes.
2
1, 1, 2, 3, 5, 7, 11, 15, 22, 29, 41, 53, 72, 92, 121, 153, 197, 245, 310, 381, 475, 579, 711, 858, 1043, 1248, 1501, 1783, 2126, 2507, 2966, 3476, 4083, 4757, 5551, 6433, 7464, 8606, 9931, 11398, 13089, 14957, 17099, 19461, 22153, 25120, 28483, 32183, 36361
OFFSET
0,3
LINKS
FORMULA
a(n) = [x^(2n) y^n] 1/Product_{j>=2} (1-y*x^A002113(j)).
a(n) = A319453(2n,n).
MAPLE
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`(i<1 or
t<1, 0, b(n, h(i-1), t)+b(n-i, h(min(n-i, i)), t-1)))
end:
a:= n-> `if`(n=0, 1, b(2*n, h(2*n), n)-b(2*n, h(2*n), n-1)):
seq(a(n), n=0..70);
CROSSREFS
Sequence in context: A238866 A035978 A319475 * A023029 A358909 A035987
KEYWORD
nonn,base
AUTHOR
Alois P. Heinz, Sep 19 2018
STATUS
approved