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 A126024 Number of subsets of {1,2,3,...,n} whose sum is a square integer (including the empty subset). 11
 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 A337745 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 January 30 12:56 EST 2023. Contains 359945 sequences. (Running on oeis4.)