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

0,4

Links

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

Formula

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

Example

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}.

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);

Crossrefs

Cf. A126024, A281871.

Sequence in context: A063072 A007626 A193297 * A240738 A047068 A167490

Adjacent sequences: A377569 A377570 A377571 * A377573 A377574 A377575

Keyword

nonn

Author

Alois P. Heinz, Nov 01 2024

Status

approved