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A154692 Triangle T(n,m) = (2^(n-m)*3^m + 2^m*3^(n-m))*binomial(n, m) read by rows, 0 <= m <= n. 6
2, 5, 5, 13, 24, 13, 35, 90, 90, 35, 97, 312, 432, 312, 97, 275, 1050, 1800, 1800, 1050, 275, 793, 3492, 7020, 8640, 7020, 3492, 793, 2315, 11550, 26460, 37800, 37800, 26460, 11550, 2315, 6817, 38064, 97776, 157248, 181440, 157248, 97776, 38064 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Row sums are A020729.

LINKS

Table of n, a(n) for n=0..43.

A. Lakhtakia, R. Messier, V. K. Varadan, V. V. Varadan, Use of combinatorial algebra for diffusion on fractals, Physical Review A, volume 34, Number 3 (1986) p. 2502, Fig. 3.

FORMULA

T(n,m) = A013620(n,m) + A013620(m,n). - R. J. Mathar, Oct 24 2011

EXAMPLE

Triangle begins

     2;

     5,     5;

    13,    24,    13;

    35,    90,    90,     35;

    97,   312,   432,    312,     97;

   275,  1050,  1800,   1800,   1050,    275;

   793,  3492,  7020,   8640,   7020,   3492,   793;

  2315, 11550, 26460,  37800,  37800,  26460, 11550,  2315;

  6817, 38064, 97776, 157248, 181440, 157248, 97776, 38064, 6817;

MAPLE

A154692 := proc(n, m)

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

end proc:

seq(seq(A154692(n, m), m=0..n), n=0..10) ; # R. J. Mathar, Oct 24 2011

MATHEMATICA

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

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

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

Flatten[%]

CROSSREFS

Sequence in context: A326532 A326637 A303355 * A309161 A144293 A174098

Adjacent sequences:  A154689 A154690 A154691 * A154693 A154694 A154695

KEYWORD

nonn,tabl,easy

AUTHOR

Roger L. Bagula and Gary W. Adamson, Jan 14 2009

STATUS

approved

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Last modified May 15 04:03 EDT 2021. Contains 343909 sequences. (Running on oeis4.)