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A154692
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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.
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6
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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; internal format)
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OFFSET
| 0,1
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COMMENTS
| Row sums are A020729.
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REFERENCES
| 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), 2502, (FIG. 3)
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FORMULA
| t(n,m) = A013620(n,m)+A013620(m,n). - R. J. Mathar, Oct 24 2011
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EXAMPLE
| 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;
20195, 125010, 356400, 635040, 816480, 816480, 635040, 356400, 125010, 20195;
60073, 409020, 1284660, 2514240, 3538080, 3919104, 3538080, 2514240, 1284660, 409020, 60073}
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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
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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[%]
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CROSSREFS
| Sequence in context: A112835 A206625 A176168 * A144293 A174098 A183419
Adjacent sequences: A154689 A154690 A154691 * A154693 A154694 A154695
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KEYWORD
| nonn,tabl,easy
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Jan 14 2009
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