A047750 If n mod 2 = 0 then m := n/2 and a(n) = (3*m)!*(5*m+1)/((m+1)!*(2*m+1)!); otherwise m := (n-1)/2, a(n) = 6*(3*m+2)!/(m!*(2*m+3)!).

1, 2, 3, 6, 11, 24, 48, 110, 231, 546, 1183, 2856, 6324, 15504, 34884, 86526, 197087, 493350, 1134705, 2861430, 6633315, 16829280, 39268320, 100134216, 234930276, 601661144, 1418201268, 3645533040, 8627761528, 22249511328

Offset

0,2

Links

Table of n, a(n) for n=0..29.

L. W. Beineke and R. E. Pippert, Enumerating dissectable polyhedra by their automorphism groups, Canad. J. Math., 26 (1974), 50-67.

Formula

From Gary W. Adamson, Jul 14 2011: (Start)

a(n) = sum of top row terms in M^n, M = the infinite square production matrix:

1, 1, 0, 0, 0, 0, ...

0, 0, 1, 0, 0, 0, ...

1, 1, 0, 1, 0, 0, ...

0, 0, 1, 0, 1, 0, ...

1, 1, 0, 1, 0, 1, ...

... (End)

8*n*(n+2)*a(n) + 4*(7*n^2 - 7*n - 17)*a(n-1) + 6*(-9*n^2 + 9*n - 17)*a(n-2) - 21*(3*n-5)*(3*n-7)*a(n-3) = 0. - R. J. Mathar, Jul 10 2013

From Robert A. Russell, Mar 20 2024: (Start)

a(n) = V(n) in the Beineke and Pippert link.

G.f.: 2*(G(z^2) - 1)/z + 2*G(z^2)^2 - G(z^2), where G(z) = 1 + z*G(z)^3 is the g.f. for A001764. (End)

Maple

series(RootOf(x*A^3-2*A^2+3*A-1, A)^2, x=0, 30);  # Mark van Hoeij, May 16 2013

Mathematica

a[0] = 1; a[1] = 2; a[n_] := a[n] = 3(2n+3)(3n-4)(3n-2)a[n-2]/(4n(n+2)(2n+1)) + (3(18n+16)a[n-1])/(4n(n+2)(2n+1)); Table[a[n], {n, 0, 29}] (* Jean-François Alcover, Dec 02 2016 *)
Table[If[OddQ[n], 6Binomial[(3n+1)/2, n+1]/(n+2), (5n+2)Binomial[3n/2, n/2] / ((n+1)(n+2))], {n, 0, 30}] (* Robert A. Russell, Feb 16 2024 *)

Prog

(PARI) a047750(n)={if(n%2, my(m=(n-1)/2); 6*(3*m+2)!/(m!*(2*m+3)!), my(m=n/2); (3*m)!*(5*m+1)/((m+1)!*(2*m+1)!))};
for(k=0, 29, print1(a047750(k), ", ")) \\ Hugo Pfoertner, Mar 07 2020

Crossrefs

Cf. A001764, A047749, A047760, A047773.

Sequence in context: A176425 A000992 A036648 * A072187 A072374 A122852

Adjacent sequences: A047747 A047748 A047749 * A047751 A047752 A047753

Keyword

nonn

Author

N. J. A. Sloane

Status

approved