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A126024 Number of subsets of {1,2,3,...,n} whose sum is a square integer (including the empty subset). 6
1, 2, 2, 3, 5, 7, 12, 20, 34, 60, 106, 190, 346, 639, 1183, 2204, 4129, 7758, 14642, 27728, 52648, 100236, 191294, 365827, 700975, 1345561, 2587057, 4981567, 9605777, 18546389, 35851756, 69382558, 134414736, 260658770, 505941852, 982896850 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

T. D. Noe and Alois P. Heinz, Table of n, a(n) for n = 0..990 (terms n=1..100 from T. D. Noe)

EXAMPLE

The subsets of {1,2,3,4,5} that sum to a square are {}, {1}, {1,3}, {4}, {2,3,4}, {1,3,5} and {4,5}. Thus a(5)=7.

MAPLE

b:= proc(n, i) option remember; (m->

      `if`(n=0 or n=m, 1, `if`(n<0 or n>m, 0, b(n, i-1)+

      `if`(i>n, 0, b(n-i, i-1)))))(i*(i+1)/2)

    end:

a:= proc(n) option remember; `if`(n<0, 0, a(n-1)+

      add(b(j^2-n, n-1), j=isqrt(n)..isqrt(n*(n+1)/2)))

    end:

seq(a(n), n=0..50);  # Alois P. Heinz, Feb 02 2017

MATHEMATICA

g[n_] := Block[{p = Product[1 + z^i, {i, n}]}, Sum[Boole[IntegerQ[Sqrt[k]]]*Coefficient[p, z, k], {k, 0, n*(n + 1)/2}]]; Array[g, 35] (* Ray Chandler, Mar 05 2007 *)

PROG

(Haskell)

import Data.List (subsequences)

a126024 = length . filter ((== 1) . a010052 . sum) .

                          subsequences . enumFromTo 1

-- Reinhard Zumkeller, Feb 22 2012, Oct 27 2010

CROSSREFS

Cf. A053632, A127542.

Cf. A181522. - Reinhard Zumkeller, Oct 27 2010

Cf. A010052, A284250.

Row sums of A281871.

Sequence in context: A060699 A284909 A062724 * A179316 A103597 A253853

Adjacent sequences:  A126021 A126022 A126023 * A126025 A126026 A126027

KEYWORD

nonn

AUTHOR

John W. Layman, Feb 27 2007

EXTENSIONS

Extended by Ray Chandler, Mar 05 2007

a(0)=1 prepended by Alois P. Heinz, Jan 30 2017

STATUS

approved

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Last modified November 13 21:28 EST 2019. Contains 329106 sequences. (Running on oeis4.)