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A091580 Number of partitions of n into decimal palindromes.

%I A091580 #18 Feb 16 2025 08:32:52
%S A091580 1,1,2,3,5,7,11,15,22,30,41,55,74,96,126,162,208,263,333,415,518,639,
%T A091580 788,962,1174,1420,1716,2060,2468,2940,3497,4137,4886,5747,6744,7885,
%U A091580 9203,10702,12424,14379,16611,19136,22009,25245,28915,33037,37688,42901,48765
%N A091580 Number of partitions of n into decimal palindromes.
%H A091580 Alois P. Heinz, <a href="/A091580/b091580.txt">Table of n, a(n) for n = 0..10000</a>
%H A091580 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PalindromicNumber.html">Palindromic Number</a>
%H A091580 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Partition.html">Partition</a>
%e A091580 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.
%p A091580 p:= proc(n) option remember; local i, s; s:= ""||n;
%p A091580       for i to iquo(length(s), 2) do if
%p A091580         s[i]<>s[-i] then return false fi od; true
%p A091580     end:
%p A091580 h:= proc(n) option remember; `if`(n<1, 0,
%p A091580      `if`(p(n), n, h(n-1)))
%p A091580     end:
%p A091580 b:= proc(n, i) option remember; `if`(n=0 or i=1, 1,
%p A091580       b(n, h(i-1))+b(n-i, h(min(n-i, i))))
%p A091580     end:
%p A091580 a:= n-> b(n, h(n)):
%p A091580 seq(a(n), n=0..100);  # _Alois P. Heinz_, Sep 19 2018
%Y A091580 Cf. A002113, A091581.
%Y A091580 Different from A088669 and from A000041.
%Y A091580 Row sums of A319453.
%K A091580 nonn,base
%O A091580 0,3
%A A091580 _Reinhard Zumkeller_, Jan 22 2004
%E A091580 a(0)=1 prepended by _Alois P. Heinz_, Sep 17 2018