A154694 Triangle T(n,m) = ((3/2)^m*2^n+(2/3)^m*3^n)*A008292(n+1,m+1) read by rows.

2, 5, 5, 13, 48, 13, 35, 330, 330, 35, 97, 2028, 4752, 2028, 97, 275, 11970, 54360, 54360, 11970, 275, 793, 69840, 557388, 1043712, 557388, 69840, 793, 2315, 407550, 5409180, 16868520, 16868520, 5409180, 407550, 2315, 6817, 2388516, 51011136

Offset

0,1

Comments

Row sums are A004123(n+2).

Links

Table of n, a(n) for n=0..38.

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

Example

2;
5, 5 ;
13, 48, 13 ;
35, 330, 330, 35 ;
97, 2028, 4752, 2028, 97 ;
275, 11970, 54360, 54360, 11970, 275 ;
793, 69840, 557388, 1043712, 557388, 69840, 793 ;
2315, 407550, 5409180, 16868520, 16868520, 5409180, 407550, 2315 ;
6817, 2388516, 51011136, 247761072, 404844480, 247761072, 51011136, 2388516, 6817 ;
20195, 14070570, 473616000, 3441251520, 8491093920, 8491093920, 3441251520, 473616000, 14070570, 20195 ;
60073, 83276472, 4357481076, 46167480576, 164067744672, 244543504896, 164067744672, 46167480576, 4357481076, 83276472, 60073 ;

Maple

A154694 := proc(n, m)
    (3^m*2^(n-m)+2^m*3^(n-m))*A008292(n+1, m+1) ;
end proc:
seq(seq( A154694(n, m), m=0..n), n=0..10) ; # R. J. Mathar, Mar 11 2024

Mathematica

Clear[t, p, q, n, m]; p = 2; q = 3;
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}];
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

Cf. A004123

Sequence in context: A174098 A183419 A305314 * A154696 A154698 A063786

Adjacent sequences: A154691 A154692 A154693 * A154695 A154696 A154697

Keyword

nonn,tabl,easy

Author

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

Extensions

Definition simplified by the Assoc. Eds. of the OEIS, Jun 07 2010

Status

approved