A154693 - OEIS

%I #3 Oct 12 2012 14:54:56

%S 2,3,3,5,16,5,9,66,66,9,17,260,528,260,17,33,1026,3624,3624,1026,33,

%T 65,4080,23820,38656,23820,4080,65,129,16302,154548,374856,374856,

%U 154548,16302,129,257,65260,993344,3529360,4998080,3529360,993344,65260,257

%N Triangle T(n,m) = ( 2^(n-m)+2^m )*A008292(n+1,m+1) read by rows.

%C Row sums are A000629(n+1).

%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. 2501, (FIG. 3)

%e The triangle starts in row n=0 with columns 0<=m<=n as:

%e 2;

%e 3, 3;

%e 5, 16, 5;

%e 9, 66, 66, 9;

%e 17, 260, 528, 260, 17;

%e 33, 1026, 3624, 3624, 1026, 33;

%e 65, 4080, 23820, 38656, 23820, 4080, 65;

%e 129, 16302, 154548, 374856, 374856, 154548, 16302, 129;

%e 257, 65260, 993344, 3529360, 4998080, 3529360, 993344, 65260, 257;

%e 513, 261354, 6314880, 32773824, 62896992, 62896992, 32773824, 6314880, 261354, 513;

%e 1025, 1046504, 39685620, 299674368, 779049120, 1006351872, 779049120, 299674368, 39685620, 1046504, 1025;

%t Clear[t, p, q, n, m]; p = 2; q = 1;

%t t[n_, m_] =(p^(n - m)*q^m + p^m*q^(n - m))*Sum[(-1)^j*Binomial[n + 2, j]*(m - j + 1)^(n + 1), {j, 0, m + 1}];

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

%t Flatten[%]

%Y Cf. A000629

%K nonn,tabl

%O 0,1

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

%E Definition simplified by the Assoc. Eds. of the OEIS - Aug 08 2010.