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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
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
KEYWORD
nonn,tabl,easy
AUTHOR
STATUS
approved

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)