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

0,3

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

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

Cf. A002113, A091581.

Different from A088669 and from A000041.

Row sums of A319453.

Sequence in context: A238867 A035988 A088669 * A325857 A023030 A246580

Adjacent sequences: A091577 A091578 A091579 * A091581 A091582 A091583

Keyword

nonn,base

Author

Reinhard Zumkeller, Jan 22 2004

Extensions

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

Status

approved