A038222 Triangle whose (i,j)-th entry is binomial(i,j)*3^(i-j)*4^j.

1, 3, 4, 9, 24, 16, 27, 108, 144, 64, 81, 432, 864, 768, 256, 243, 1620, 4320, 5760, 3840, 1024, 729, 5832, 19440, 34560, 34560, 18432, 4096, 2187, 20412, 81648, 181440, 241920, 193536, 86016, 16384, 6561, 69984, 326592, 870912, 1451520

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• tabl
• easy

Links

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

Programs

Mathematica

Table[Binomial[i,j]3^(i-j) 4^j,{i,0,10},{j,0,i}]//Flatten (* Harvey P. Dale, Oct 02 2021 *)

Formula

G.f.: 1/(1 - 3*x - 4*x*y). - Ilya Gutkovskiy, Apr 21 2017