A091580 Number of partitions of n into decimal palindromes.

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

Author

Reinhard Zumkeller, Jan 22 2004

Keywords

• nonn
• base

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Palindromic Number
• Eric Weisstein's World of Mathematics, Partition

Crossrefs

Cf. A002113, A091581.

Different from A088669 and from A000041.

Row sums of A319453.

Programs

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

Extensions

a(0)=1 prepended by Alois P. Heinz, Sep 17 2018