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 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 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

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Last modified June 1 18:43 EDT 2020. Contains 334762 sequences. (Running on oeis4.)