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%I A154690 #15 Jan 06 2019 06:08:26
%S A154690 2,3,3,5,8,5,9,18,18,9,17,40,48,40,17,33,90,120,120,90,33,65,204,300,
%T A154690 320,300,204,65,129,462,756,840,840,756,462,129,257,1040,1904,2240,
%U A154690 2240,2240,1904,1040,257,513,2322,4752,6048,6048,6048,6048,4752,2322,513
%N A154690 Triangle read by rows: T(n,m) = (2^(n-m) + 2^m)*binomial(n,m), 0 <= m <= n.
%C A154690 Row sums are A025192(n+1).
%H A154690 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 A154690 T(n,m) = A007318(n,m)*(2^(n-m) + 2^m).
%e A154690      2;
%e A154690      3,    3;
%e A154690      5,    8,     5;
%e A154690      9,   18,    18,     9;
%e A154690     17,   40,    48,    40,    17;
%e A154690     33,   90,   120,   120,    90,    33;
%e A154690     65,  204,   300,   320,   300,   204,    65;
%e A154690    129,  462,   756,   840,   840,   756,   462,   129;
%e A154690    257, 1040,  1904,  2240,  2240,  2240,  1904,  1040,   257;
%e A154690    513, 2322,  4752,  6048,  6048,  6048,  6048,  4752,  2322,  513;
%e A154690   1025, 5140, 11700, 16320, 16800, 16128, 16800, 16320, 11700, 5140, 1025;
%p A154690 A154690 := proc(n,m) binomial(n,m)*(2^(n-m)+2^m) ; end proc: # _R. J. Mathar_, Jan 13 2011
%t A154690 t[n_, m_] := (2^(n - m) + 2^m) Binomial[n, m]; Table[ t[n, m], {n, 0, 9}, {m, 0, n}] // Flatten
%t A154690 (* alternate program *)
%t A154690 Table[Table[ Sum[Binomial[n, m]*Binomial[m, k] + Binomial[n, n - m]*Binomial[m, m - k], {k, 0, n}]/2, {m, 0, n}]
%t A154690 + Reverse[ Table[Sum[ Binomial[n, m]*Binomial[m, k] + Binomial[n, n - m]*Binomial[m, m - k], {k, 0, n}]/2, {m, 0, n}]], {n, 0, 10}] (* _Roger L. Bagula_, Oct 14 2010 *)
%Y A154690 Cf. A025192.
%K A154690 nonn,tabl,easy
%O A154690 0,1
%A A154690 _Roger L. Bagula_ and _Gary W. Adamson_, Jan 14 2009

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