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Triangle T(n,m) = (2^(n-m)*3^m + 2^m*3^(n-m))*binomial(n, m) read by rows, 0 <= m <= n.
6

%I #17 May 09 2019 01:08:50

%S 2,5,5,13,24,13,35,90,90,35,97,312,432,312,97,275,1050,1800,1800,1050,

%T 275,793,3492,7020,8640,7020,3492,793,2315,11550,26460,37800,37800,

%U 26460,11550,2315,6817,38064,97776,157248,181440,157248,97776,38064

%N Triangle T(n,m) = (2^(n-m)*3^m + 2^m*3^(n-m))*binomial(n, m) read by rows, 0 <= m <= n.

%C Row sums are A020729.

%H A. Lakhtakia, R. Messier, V. K. Varadan, V. V. Varadan, <a href="http://dx.doi.org/10.1103/PhysRevA.34.2501">Use of combinatorial algebra for diffusion on fractals</a>, Physical Review A, volume 34, Number 3 (1986) p. 2502, Fig. 3.

%F T(n,m) = A013620(n,m) + A013620(m,n). - _R. J. Mathar_, Oct 24 2011

%e Triangle begins

%e 2;

%e 5, 5;

%e 13, 24, 13;

%e 35, 90, 90, 35;

%e 97, 312, 432, 312, 97;

%e 275, 1050, 1800, 1800, 1050, 275;

%e 793, 3492, 7020, 8640, 7020, 3492, 793;

%e 2315, 11550, 26460, 37800, 37800, 26460, 11550, 2315;

%e 6817, 38064, 97776, 157248, 181440, 157248, 97776, 38064, 6817;

%p A154692 := proc(n,m)

%p (2^(n-m)*3^m+2^m*3^(n-m))*binomial(n,m) ;

%p end proc:

%p seq(seq(A154692(n,m),m=0..n),n=0..10) ; # _R. J. Mathar_, Oct 24 2011

%t Clear[t, p, q, n, m]; p = 2; q = 3;

%t t[n_, m_] = (p^(n - m)*q^m + p^m*q^(n - m))*Binomial[n, m];

%t Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];

%t Flatten[%]

%K nonn,tabl,easy

%O 0,1

%A _Roger L. Bagula_ and _Gary W. Adamson_, Jan 14 2009