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

0, 1, 1, 3, 7, 12, 30, 61, 124, 247, 491, 980, 1962, 3949, 7916, 15863, 31815, 63692, 127570, 255529, 511627, 1024421, 2051038, 4105848, 8218842, 16450989, 32926094, 65897438, 131879440, 263915641, 528125412, 1056802576, 2114639286, 4231226460, 8466125334, 16939180972

Offset: 0

Author

Alois P. Heinz, Nov 01 2024

Keywords

• nonn

Examples

			a(4) = 7: {1}, {4}, {1,3}, {2,3,4}.
a(5) = 12: {1}, {4}, {1,3}, {4,5}, {1,3,5}, {2,3,4}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A126024, A281871.

Programs

Maple

b:= proc(n, s) option remember; `if`(n=0, `if`(issqr(s),
      [1, 0], 0), b(n-1, s)+(p-> p+[0, p[1]])(b(n-1, s+n)))
    end:
a:= n-> b(n, 0)[2]:
seq(a(n), n=0..35);

Formula

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