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A047776 Number of dissectable polyhedra with symmetry of type A. 2
0, 0, 0, 0, 2, 11, 71, 370, 2005, 10682, 58167, 320116, 1789210, 10121965, 57933469, 334919626, 1953800059, 11489466014, 68053583772, 405713887061, 2433000197471, 14668527134167, 88869448492895, 540834097467624, 3304961431043989, 20273201718862728, 124798671079300720, 770762029389852807 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..28.

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

FORMULA

Reference gives complicated recurrence.

MATHEMATICA

Table[If[n < 5, 0, Binomial[3 n, 2 n + 2]/(3 n (n - 1))

    - If[OddQ[n], Binomial[3 n/2 - 1/2, n + 1] 3/(n - 1),

     7 Binomial[3 n/2, n + 1]/(3 n)]

    - Switch[Mod[n, 3], 1, Binomial[n - 1, 2 n/3 + 1/3]/(n - 1), 2,

     Binomial[n - 1, 2 n/3 + 2/3]/(n - 2), _, 0]

    + Switch[Mod[n, 4], 1, Binomial[3 n/4 - 3/4, n/2 + 1/2] 2/(3 (n - 1))

      + Binomial[3 n/4 + 1/4, n/2 + 3/2] 4/(n - 1) +

      Binomial[3 n/4 - 3/4, n/2 + 1/2] 4/(n + 3), 2,

     Binomial[3 n/4 - 1/2, n/2 + 1] 8/(n - 2), 3,

     Binomial[3 n/4 - 1/4, n/2 + 3/2] 12/(n - 3), 0,

     Binomial[3 n/4 - 1, n/2 + 1] 12/(n - 4)] +

    Switch[Mod[n, 6], 1, Binomial[n/2 - 1/2, n/3 + 2/3] 6/(n - 1), 2,

     Binomial[n/2 - 1, n/3 + 1/3] 4/(n - 2) +

      Binomial[n/2, n/3 + 4/3] 6/(n - 2) +

      Binomial[n/2 - 1, n/3 + 1/3] 6/(n + 4), 4,

     Binomial[n/2 - 1, n/3 + 2/3] 12/(n - 4), 5,

     Binomial[n/2 - 1/2, n/3 + 1/3] 9/(n + 4), _, 0] +

    Switch[Mod[n, 12], 2, -Binomial[n/4 - 1/2, n/6 + 2/3] 12/(n - 2), 5,

     Binomial[n/4 - 5/4, n/6 - 5/6] 2/(n + 1),

     8, -Binomial[n/4 - 1, n/6 - 1/3] 12/(n + 4), _, 0] -

    Switch[Mod[n, 24], 5, Binomial[n/8 - 5/8, n/12 - 5/12] 12/(n + 7), 17,

     Binomial[n/8 - 9/8, n/12 - 5/12] 24/(n + 7), _, 0]]/2, {n, 1, 60}]

CROSSREFS

Cf. A027610.

Sequence in context: A135166 A118347 A250887 * A214692 A186633 A291301

Adjacent sequences:  A047773 A047774 A047775 * A047777 A047778 A047779

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified December 13 05:16 EST 2018. Contains 318082 sequences. (Running on oeis4.)