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A038233 Triangle whose (i,j)-th entry is binomial(i,j)*4^(i-j)*3^j. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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 A046162 A060509

Adjacent sequences:  A038230 A038231 A038232 * A038234 A038235 A038236

KEYWORD

nonn,tabl,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified September 28 13:24 EDT 2020. Contains 337393 sequences. (Running on oeis4.)