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A377572 Total number of elements (with multiplicity) in all subsets of [n] having a square element sum.

%I A377572 #17 Nov 07 2024 19:16:44
%S A377572 0,1,1,3,7,12,30,61,124,247,491,980,1962,3949,7916,15863,31815,63692,
%T A377572 127570,255529,511627,1024421,2051038,4105848,8218842,16450989,
%U A377572 32926094,65897438,131879440,263915641,528125412,1056802576,2114639286,4231226460,8466125334,16939180972
%N A377572 Total number of elements (with multiplicity) in all subsets of [n] having a square element sum.
%H A377572 Alois P. Heinz, <a href="/A377572/b377572.txt">Table of n, a(n) for n = 0..500</a>
%F A377572 a(n) = Sum_{k=0..n} k * A281871(n,k).
%e A377572 a(4) = 7: {1}, {4}, {1,3}, {2,3,4}.
%e A377572 a(5) = 12: {1}, {4}, {1,3}, {4,5}, {1,3,5}, {2,3,4}.
%p A377572 b:= proc(n, s) option remember; `if`(n=0, `if`(issqr(s),
%p A377572       [1, 0], 0), b(n-1, s)+(p-> p+[0, p[1]])(b(n-1, s+n)))
%p A377572     end:
%p A377572 a:= n-> b(n, 0)[2]:
%p A377572 seq(a(n), n=0..35);
%Y A377572 Cf. A126024, A281871.
%K A377572 nonn
%O A377572 0,4
%A A377572 _Alois P. Heinz_, Nov 01 2024