The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A154690 Triangle read by rows: T(n,m) = (2^(n-m) + 2^m)*binomial(n,m), 0 <= m <= n. 6
 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 (list; table; graph; refs; listen; history; text; internal format)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 26 08:25 EDT 2024. Contains 372813 sequences. (Running on oeis4.)