A038233 Triangle whose (i,j)-th entry is binomial(i,j)*4^(i-j)*3^j.

1, 4, 3, 16, 24, 9, 64, 144, 108, 27, 256, 768, 864, 432, 81, 1024, 3840, 5760, 4320, 1620, 243, 4096, 18432, 34560, 34560, 19440, 5832, 729, 16384, 86016, 193536, 241920, 181440, 81648, 20412, 2187, 65536, 393216, 1032192, 1548288

Offset

0,2

Comments

T(i,j) is the number of sequences (X_1, X_2, X_3) of subsets of {1,2,...,i} such that X_1 intersect X_2 intersect X_3 is empty and X_3 contains exactly j elements. Cf. Stanley reference. - Geoffrey Critzer, Jan 11 2016

References

B. N. Cyvin et al., Isomer enumeration of unbranched catacondensed polygonal systems with pentagons and heptagons, Match, No. 34 (Oct 1996), pp. 109-121.

R. P. Stanley, Enumerative Combinatorics Vol I, Cambridge Univ. Press, 1997, page 11.

Links

Table of n, a(n) for n=0..39.

Formula

E.g.f.: exp(4*x + 3*y*x). - Geoffrey Critzer, Jan 11 2016

Example

1;
4,    3;
16,   24,    9;
64,   144,   108,   27;
256,  768,   864,   432,   81;
1024, 3840,  5760,  4320,  1620,  243;
4096, 18432, 34560, 34560, 19440, 5832, 729;

Mathematica

nn = 10; Map[Select[#, # > 0 &] &, Range[0, nn]! CoefficientList[
Series[Exp[3 x + 3 y x] Exp[x], {x, 0, nn}], {x, y}]] // Grid (* Geoffrey Critzer, Jan 11 2016 *)

Crossrefs

Cf. A038207, A038285.

Sequence in context: A288368 A288595 A288067 * A176737 A370566 A046162

Adjacent sequences: A038230 A038231 A038232 * A038234 A038235 A038236

Keyword

nonn,tabl,easy

Author

N. J. A. Sloane.

Status

approved