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 A029600 Numbers in the (2,3)-Pascal triangle (by row). 28
 1, 2, 3, 2, 5, 3, 2, 7, 8, 3, 2, 9, 15, 11, 3, 2, 11, 24, 26, 14, 3, 2, 13, 35, 50, 40, 17, 3, 2, 15, 48, 85, 90, 57, 20, 3, 2, 17, 63, 133, 175, 147, 77, 23, 3, 2, 19, 80, 196, 308, 322, 224, 100, 26, 3, 2, 21, 99, 276, 504, 630, 546, 324, 126, 29, 3, 2, 23, 120, 375, 780 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Reverse of A029618. - Philippe Deléham, Nov 21 2006 Triangle T(n,k), read by rows, given by (2,-1,0,0,0,0,0,0,0,...) DELTA (3,-2,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938. - Philippe Deléham, Oct 10 2011 Row n: expansion of (2+3x)*(1+x)^(n-1), n>0. - Philippe Deléham, Oct 10 2011. For n > 0: T(n,k) = A029635(n,k) + A007318(n,k), 0 <= k <= n. - Reinhard Zumkeller, Apr 16 2012 For a closed-form formula for generalized Pascal's triangle see A228576. - Boris Putievskiy, Sep 04 2013 For n>0, row sums = 5*2^(n-1). Generally, for all (a,b)-Pascal triangles, row sums are (a+b)*2^(n-1), n>0. - Bob Selcoe, Mar 28 2015 LINKS Reinhard Zumkeller, Rows n=0..150 of triangle, flattened FORMULA T(n,k) = T(n-1,k-1) + T(n-1,k) with T(0,0)=1, T(n,0)=2, T(0,k)=3; n, k > 0. - Boris Putievskiy, Sep 04 2013 G.f.: (-1-2*x*y-x)/(-1+x*y+x). - R. J. Mathar, Aug 11 2015 EXAMPLE First few rows are: 1 2  3 2  5  3 2  7  8  3 2  9 15 11  3 ... PROG (Haskell) a029600 n k = a029600_tabl !! n !! k a029600_row n = a029600_tabl !! n a029600_tabl = [1] : iterate    (\row -> zipWith (+) ([0] ++ row) (row ++ [0])) [2, 3] -- Reinhard Zumkeller, Apr 08 2012 CROSSREFS Cf. A007318 (Pascal's triangle), A029618, A084938, A228196, A228576. Sequence in context: A049805 A104887 A064886 * A169616 A111076 A162398 Adjacent sequences:  A029597 A029598 A029599 * A029601 A029602 A029603 KEYWORD nonn,tabl,easy AUTHOR EXTENSIONS More terms from James A. Sellers STATUS approved

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Last modified October 23 22:04 EDT 2018. Contains 316541 sequences. (Running on oeis4.)