A275209 Expansion of (A(x)^2+A(x^2))/2 where A(x) = A001006(x)-1.

0, 0, 1, 2, 7, 17, 49, 129, 358, 970, 2679, 7364, 20414, 56634, 157877, 441084, 1236496, 3474672, 9790403, 27648486, 78256907, 221951037, 630723367, 1795576937, 5120487946, 14625574662, 41837955145, 119851980508, 343798121799, 987445317761, 2839518519233

Offset

0,4

Comments

Analog of A274934 with Motzkin numbers replacing connected graph counts.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

a(2n+1) = A275210(2n+1).

Maple

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=1..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

Mathematica

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, 1, 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 *)

Crossrefs

Cf. A275210.

Sequence in context: A367687 A085411 A180665 * A007049 A133407 A182667

Adjacent sequences: A275206 A275207 A275208 * A275210 A275211 A275212

Keyword

nonn

Author

R. J. Mathar, Jul 19 2016

Status

approved