A377572 - OEIS

%I #17 Nov 07 2024 19:16:44

%S 0,1,1,3,7,12,30,61,124,247,491,980,1962,3949,7916,15863,31815,63692,

%T 127570,255529,511627,1024421,2051038,4105848,8218842,16450989,

%U 32926094,65897438,131879440,263915641,528125412,1056802576,2114639286,4231226460,8466125334,16939180972

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

%H Alois P. Heinz, <a href="/A377572/b377572.txt">Table of n, a(n) for n = 0..500</a>

%F a(n) = Sum_{k=0..n} k * A281871(n,k).

%e a(4) = 7: {1}, {4}, {1,3}, {2,3,4}.

%e a(5) = 12: {1}, {4}, {1,3}, {4,5}, {1,3,5}, {2,3,4}.

%p b:= proc(n, s) option remember; `if`(n=0, `if`(issqr(s),

%p       [1, 0], 0), b(n-1, s)+(p-> p+[0, p[1]])(b(n-1, s+n)))

%p     end:

%p a:= n-> b(n, 0)[2]:

%p seq(a(n), n=0..35);

%Y Cf. A126024, A281871.

%K nonn

%O 0,4

%A _Alois P. Heinz_, Nov 01 2024