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A339441
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Number of compositions (ordered partitions) of n into an even number of distinct triangular numbers.
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2
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1, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 4, 0, 2, 0, 24, 2, 2, 0, 2, 26, 0, 2, 0, 26, 0, 28, 24, 0, 26, 24, 2, 2, 50, 2, 48, 0, 26, 26, 0, 48, 28, 72, 2, 26, 48, 4, 48, 48, 24, 74, 770, 2, 50, 48, 50, 26, 72, 720, 98, 74, 26, 74, 48, 770, 74, 768, 26, 122, 792, 72
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OFFSET
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0,5
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LINKS
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EXAMPLE
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a(20) = 24 because we have [10, 6, 3, 1] (24 permutations).
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MAPLE
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b:= proc(n, i, p) option remember; `if`(n=0, irem(1+p, 2)*p!, (t->
`if`(t>n, 0, b(n, i+1, p)+b(n-t, i+1, p+1)))(i*(i+1)/2))
end:
a:= n-> b(n, 1, 0):
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MATHEMATICA
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b[n_, i_, p_] := b[n, i, p] = If[n == 0, Mod[1 + p, 2]*p!, With[{t = i(i+1)/2}, If[t > n, 0, b[n, i + 1, p] + b[n - t, i + 1, p + 1]]]];
a[n_] := b[n, 1, 0];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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