A154690 Triangle read by rows: T(n,m) = (2^(n-m) + 2^m)*binomial(n,m), 0 <= m <= n.

2, 3, 3, 5, 8, 5, 9, 18, 18, 9, 17, 40, 48, 40, 17, 33, 90, 120, 120, 90, 33, 65, 204, 300, 320, 300, 204, 65, 129, 462, 756, 840, 840, 756, 462, 129, 257, 1040, 1904, 2240, 2240, 2240, 1904, 1040, 257, 513, 2322, 4752, 6048, 6048, 6048, 6048, 4752, 2322, 513

Offset

0,1

Comments

Row sums are A025192(n+1).

Links

Table of n, a(n) for n=0..54.

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) = A007318(n,m)*(2^(n-m) + 2^m).

Example

     2;
     3,    3;
     5,    8,     5;
     9,   18,    18,     9;
    17,   40,    48,    40,    17;
    33,   90,   120,   120,    90,    33;
    65,  204,   300,   320,   300,   204,    65;
   129,  462,   756,   840,   840,   756,   462,   129;
   257, 1040,  1904,  2240,  2240,  2240,  1904,  1040,   257;
   513, 2322,  4752,  6048,  6048,  6048,  6048,  4752,  2322,  513;
  1025, 5140, 11700, 16320, 16800, 16128, 16800, 16320, 11700, 5140, 1025;

Maple

A154690 := proc(n, m) binomial(n, m)*(2^(n-m)+2^m) ; end proc: # R. J. Mathar, Jan 13 2011

Mathematica

t[n_, m_] := (2^(n - m) + 2^m) Binomial[n, m]; Table[ t[n, m], {n, 0, 9}, {m, 0, n}] // Flatten
(* alternate program *)
Table[Table[ Sum[Binomial[n, m]*Binomial[m, k] + Binomial[n, n - m]*Binomial[m, m - k], {k, 0, n}]/2, {m, 0, n}]
+ Reverse[ Table[Sum[ Binomial[n, m]*Binomial[m, k] + Binomial[n, n - m]*Binomial[m, m - k], {k, 0, n}]/2, {m, 0, n}]], {n, 0, 10}] (* Roger L. Bagula, Oct 14 2010 *)

Crossrefs

Cf. A025192.

Sequence in context: A295379 A295352 A295606 * A046937 A247309 A069831

Adjacent sequences: A154687 A154688 A154689 * A154691 A154692 A154693

Keyword

nonn,tabl,easy

Author

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

Status

approved