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A091580
Number of partitions of n into decimal palindromes.
8
1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 41, 55, 74, 96, 126, 162, 208, 263, 333, 415, 518, 639, 788, 962, 1174, 1420, 1716, 2060, 2468, 2940, 3497, 4137, 4886, 5747, 6744, 7885, 9203, 10702, 12424, 14379, 16611, 19136, 22009, 25245, 28915, 33037, 37688, 42901, 48765
OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Palindromic Number
Eric Weisstein's World of Mathematics, Partition
EXAMPLE
n=12: there are A000041(12)=77 partitions of 12, 3 of them contain non-palindromes: 12=10+2, 12=10+1+1 and 12 itself, therefore a(12)=77-3=74.
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) option remember; `if`(n=0 or i=1, 1,
b(n, h(i-1))+b(n-i, h(min(n-i, i))))
end:
a:= n-> b(n, h(n)):
seq(a(n), n=0..100); # Alois P. Heinz, Sep 19 2018
CROSSREFS
Different from A088669 and from A000041.
Row sums of A319453.
Sequence in context: A238867 A035988 A088669 * A325857 A023030 A246580
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Jan 22 2004
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Sep 17 2018
STATUS
approved