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A341206 Number of ways to write n as an ordered sum of 9 nonzero decimal palindromes.

%I A341206 #10 Feb 07 2021 13:14:12
%S A341206 1,9,45,165,495,1287,3003,6435,12870,24301,43686,75249,124809,200115,
%T A341206 311157,470415,693000,996633,1401436,1929465,2603979,3448440,4485267,
%U A341206 5734395,7211718,8927523,10885050,13079257,15496065,18112050,20894757,23803659,26791749,29807697,32798448
%N A341206 Number of ways to write n as an ordered sum of 9 nonzero decimal palindromes.
%H A341206 Alois P. Heinz, <a href="/A341206/b341206.txt">Table of n, a(n) for n = 9..10000</a>
%p A341206 p:= proc(n) option remember; local i, s; s:= ""||n;
%p A341206       for i to iquo(length(s), 2) do if
%p A341206         s[i]<>s[-i] then return false fi od; true
%p A341206     end:
%p A341206 b:= proc(n, t) option remember; `if`(n=0, `if`(t=0, 1, 0),
%p A341206       `if`(t<1, 0, add(`if`(p(j), b(n-j, t-1), 0), j=1..n)))
%p A341206     end:
%p A341206 a:= n-> b(n, 9):
%p A341206 seq(a(n), n=9..43);  # _Alois P. Heinz_, Feb 07 2021
%t A341206 nmax = 43; CoefficientList[Series[Sum[Boole[PalindromeQ[k]] x^k, {k, 1, nmax}]^9, {x, 0, nmax}], x] // Drop[#, 9] &
%Y A341206 Cf. A002113, A136522, A319474, A341167, A341184, A341191, A341192, A341193, A341203, A341204, A341205, A341207.
%K A341206 nonn,base
%O A341206 9,2
%A A341206 _Ilya Gutkovskiy_, Feb 06 2021