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A275207
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Expansion of (A(x)^2+A(x^2))/2 where A(x) = A001006(x).
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2
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1, 1, 3, 6, 16, 38, 100, 256, 681, 1805, 4867, 13162, 35925, 98469, 271511, 751656, 2089963, 5831451, 16326785, 45847770, 129108926, 364498596, 1031486590, 2925337352, 8313215743, 23668977163, 67507773621, 192859753310, 551821400008, 1581188102590
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OFFSET
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0,3
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COMMENTS
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Analog of A275165 with Motzkin numbers replacing connected graph counts.
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..1000
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FORMULA
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a(2n+1) = A275208(2n+1).
Conjecture: a(2n+1) = A026940(n+1).
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MAPLE
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b:= proc(n) option remember; `if`(n<2, 1,
((3*(n-1))*b(n-2)+(1+2*n)*b(n-1))/(n+2))
end:
a:= proc(n) option remember; add(b(j)*b(n-j), j=0..n/2)-
`if`(n::odd, 0, (t-> t*(t-1)/2)(b(n/2)))
end:
seq(a(n), n=0..40); # Alois P. Heinz, Jul 19 2016
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MATHEMATICA
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b[n_] := b[n] = If[n<2, 1, ((3*(n-1))*b[n-2] + (1+2*n)*b[n-1])/(n+2)];
a[n_] := a[n] = Sum[b[j]*b[n-j], {j, 0, n/2}] - If[OddQ[n], 0, Function[t, t*(t-1)/2][b[n/2]]];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, May 16 2017, after Alois P. Heinz *)
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CROSSREFS
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Cf. A275208, A026940.
Sequence in context: A190735 A096588 A256943 * A073079 A143560 A279685
Adjacent sequences: A275204 A275205 A275206 * A275208 A275209 A275210
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KEYWORD
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nonn
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AUTHOR
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R. J. Mathar, Jul 19 2016
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STATUS
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approved
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