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 A087322 Triangle T read by rows: T(n, 1) = 2*n + 1. For 1 < k <= n, T(n, k) = 2*T(n,k-1) + 1. 3
 3, 5, 11, 7, 15, 31, 9, 19, 39, 79, 11, 23, 47, 95, 191, 13, 27, 55, 111, 223, 447, 15, 31, 63, 127, 255, 511, 1023, 17, 35, 71, 143, 287, 575, 1151, 2303, 19, 39, 79, 159, 319, 639, 1279, 2559, 5119, 21, 43, 87, 175, 351, 703, 1407, 2815, 5631, 11263, 23, 47, 95 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS With T(n,0) = n for n >= 0, this becomes J. M. Bergot's triangular array in the definition of A190730. - Petros Hadjicostas, Feb 15 2021 LINKS FORMULA T(n, k) = (n + 1)*2^k - 1 for n >= 1 and 1 <= k <= n. From Petros Hadjicostas, Feb 15 2021: (Start) Sum_{k=1..n} T(n,k) = A190730(n). T(n,2) = 4*n + 3 for n >= 2. T(n,n) = A087323(n). T(n,n-1) = A099035(n) = (n+1)*2^(n-1) - 1 for n >= 2. Recurrence: T(n,k) = 3*T(n,k-1) - 2*T(n,k-2) for n >= 2 and 2 <= k <= n with initial conditions the values of T(n, 1) and T(n,2). Bivariate o.g.f.: Sum_{n,k>=1} T(n,k)*x^n*y^k = (4*x^3*y^2 - 2*x^2*y - 4*x*y - x + 3)*x*y/((1 - 2*x*y)^2*(1 - x*y)*(1 - x)^2). (End) EXAMPLE Triangle T(n,k) (with rows n >= 1 and columns k = 1..n) begins:    3;    5, 11;    7, 15, 31;    9, 19, 39,  79;   11, 23, 47,  95, 191;   13, 27, 55, 111, 223, 447;   15, 31, 63, 127, 255, 511, 1023;   17, 35, 71, 143, 287, 575, 1151, 2303;   19, 39, 79, 159, 319, 639, 1279, 2559, 5119;   ... CROSSREFS Cf. A087323, A099035, A190730. Sequence in context: A073653 A225487 A145398 * A094747 A300783 A287939 Adjacent sequences:  A087319 A087320 A087321 * A087323 A087324 A087325 KEYWORD nonn,tabl,easy AUTHOR Amarnath Murthy, Sep 03 2003 EXTENSIONS Edited and extended by David Wasserman, May 06 2005 Name edited by Petros Hadjicostas, Feb 15 2021 STATUS approved

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Last modified June 13 06:07 EDT 2021. Contains 344981 sequences. (Running on oeis4.)