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A216188 Number of unordered pairs of anagrammatic (positive) integers adding to n.

%I A216188 #30 Oct 30 2023 07:32:41
%S A216188 0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,
%T A216188 0,1,0,1,0,1,0,1,0,2,0,1,0,1,0,1,0,1,0,1,2,1,0,1,0,1,0,1,0,1,0,3,0,1,
%U A216188 0,1,0,1,0,1,0,1,3,1,0,1,0,1,0,1,0,1,0
%N A216188 Number of unordered pairs of anagrammatic (positive) integers adding to n.
%C A216188 Two positive integers are here defined as "anagrammatic" if (in base 10) they have the same number of 0 digits, 1 digits, 2 digits, ..., 9 digits. Thus, 123 and 231 are anagrammatic, but not 301 and 013, as leading zeros are omitted.
%H A216188 Christian Schulz, <a href="/A216188/b216188.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from T. D. Noe)
%e A216188 For n = 88, the a(88) = 4 pairs are {17,71}, {26,62}, {35,53}, and {44,44}. For n = 609, the a(609) = 1 pair is {237,372}.
%p A216188 getDigit := (n,k) -> floor(n/10^k) mod 10; getMaxDigit := n -> floor(log10(n)) + 1; getDigitMultiset := n -> convert([seq(getDigit(n,k),k=0..getMaxDigit(n)-1)],multiset); isAnagram := (m,n) -> evalb(getDigitMultiset(m) = getDigitMultiset(n)); A216188 := n -> convert([seq(eval(isAnagram(k,n-k),[true=1,false=0]),k=1..floor(n/2))],`+`); seq(A216188(n),n=1..50)
%t A216188 IsAnagram[x_, y_, b_: 10] := Sort[Permutations[IntegerDigits[x, b]]] == Sort[Permutations[IntegerDigits[y, b]]]; FindAnagramSums[n_, b_: 10] := Select[Table[{k, n - k}, {k, 0, Floor[n/2]}], IsAnagram[#[[1]], #[[2]], b] &]; Table[Length[FindAnagramSums[n]], {n, 1, 200}]
%K A216188 nonn,base
%O A216188 1,44
%A A216188 _Christian Schulz_, Mar 11 2013