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A126024
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Number of subsets of {1,2,3,...,n} whose sum is a square integer (including the empty subset).
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11
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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)
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OFFSET
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0,2
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LINKS
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T. D. Noe and Alois P. Heinz, Table of n, a(n) for n = 0..990 (terms n=1..100 from T. D. Noe)
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EXAMPLE
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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.
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(Haskell)
import Data.List (subsequences)
a126024 = length . filter ((== 1) . a010052 . sum) .
subsequences . enumFromTo 1
-- Reinhard Zumkeller, Feb 22 2012, Oct 27 2010
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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John W. Layman, Feb 27 2007
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EXTENSIONS
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Extended by Ray Chandler, Mar 05 2007
a(0)=1 prepended by Alois P. Heinz, Jan 30 2017
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STATUS
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approved
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