login
Triangle whose (i,j)-th entry is binomial(i,j)*4^(i-j)*4^j.
1

%I #15 Aug 28 2017 06:33:07

%S 1,4,4,16,32,16,64,192,192,64,256,1024,1536,1024,256,1024,5120,10240,

%T 10240,5120,1024,4096,24576,61440,81920,61440,24576,4096,16384,114688,

%U 344064,573440,573440,344064,114688,16384,65536,524288

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

%C Also the absolute values of the coefficients of the Belyi Polynomial P_(i,i)(x). - _R. J. Mathar_, Oct 16 2008

%H I. Bauer, F. Catanese, F. Grunewald, <a href="http://dx.doi.org/10.1007/s00009-006-0069-7">Chebycheff and Belyi Polynomials, Dessins de'Enfants, Beauville Surfaces and Group Theory</a>, Med. J. Math. vol 3 no 2 (2006) 121-146. [From _R. J. Mathar_, Oct 16 2008]

%H B. N. Cyvin et al., <a href="http://match.pmf.kg.ac.rs/electronic_versions/Match34/match34_109-121.pdf">Isomer enumeration of unbranched catacondensed polygonal systems with pentagons and heptagons</a>, Match, No. 34 (Oct 1996), pp. 109-121.

%F G.f.: 1/(1 - 4*x - 4*x*y). - _Ilya Gutkovskiy_, Apr 21 2017

%e 1 ;

%e 4 4 ;

%e 16 32 16 ;

%e 64 192 192 64 ;

%e 256 1024 1536 1024 256 ;

%e 1024 5120 10240 10240 5120 1024 ;

%e 4096 24576 61440 81920 61440 24576 4096 ;

%e 16384 114688 344064 573440 573440 344064 114688 16384 ;

%e 65536 524288 1835008 3670016 4587520 3670016 1835008 524288 65536 ;

%e 262144 2359296 9437184 22020096 33030144 33030144 22020096 9437184 2359296 262144 ;

%K nonn,tabl,easy

%O 0,2

%A _N. J. A. Sloane_.