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Number of compositions (ordered partitions) of n into decimal palindromes (A002113).
3

%I #8 Jun 25 2021 01:40:04

%S 1,1,2,4,8,16,32,64,128,256,511,1022,2042,4081,8156,16300,32576,65104,

%T 130112,260032,519681,1038595,2075660,4148259,8290402,16568581,

%U 33112734,66176648,132255728,264316464,528243231,1055707644,2109858797,4216606912,8426997041,16841569684,33658308890,67266993433

%N Number of compositions (ordered partitions) of n into decimal palindromes (A002113).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PalindromicNumber.html">Palindromic Number</a>

%H <a href="/index/Pac#palindromes">Index entries for sequences related to palindromes</a>

%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>

%F G.f.: 1/(1 - Sum_{k>=2} x^A002113(k)).

%e a(4) = 8 because we have [4], [3, 1], [2, 2], [2, 1, 1], [1, 3], [1, 2, 1], [1, 1, 2] and [1, 1, 1, 1].

%t nmax = 37; CoefficientList[Series[1/(1 - Sum[Boole[PalindromeQ[k]] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]

%Y Cf. A002113, A091580, A091581, A260254, A261422.

%K nonn,base

%O 0,3

%A _Ilya Gutkovskiy_, Feb 19 2017