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 A162741 Fibonacci-Pascal triangle; same as Pascal triangle, but beginning another Pascal triangle to the right of each row starting at row 2. 19
 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 3, 4, 3, 2, 1, 1, 1, 4, 7, 7, 5, 3, 2, 1, 1, 1, 5, 11, 14, 12, 8, 5, 3, 2, 1, 1, 1, 6, 16, 25, 26, 20, 13, 8, 5, 3, 2, 1, 1, 1, 7, 22, 41, 51, 46, 33, 21, 13, 8, 5, 3, 2, 1, 1, 1, 8, 29, 63, 92, 97, 79, 54, 34, 21, 13, 8, 5, 3, 2, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS Intertwined Pascal-triangles; the first five rows seen as numbers in decimal representation: row(n) = 110*row(n-1) + 1. - corrected by Reinhard Zumkeller, Jul 16 2013 LINKS Reinhard Zumkeller, Rows n = 1..100 of triangle, flattened Richard L. Ollerton and Anthony G. Shannon, Some properties of generalized Pascal squares and triangles, Fib. Q., 36 (1998), 98-109. See Table 3. FORMULA T(n,k) = T(n-1,k-1) + T(n-1,k), T(n,1)=1 and for n>1: T(n,2*n-2) = T(n,2*n-1)=1. - Reinhard Zumkeller, Jul 16 2013 EXAMPLE .                                           1 .                                       1,  1, 1 .                                   1,  2,  2, 1, 1 .                               1,  3,  4,  3, 2, 1, 1 .                           1,  4,  7,  7,  5, 3, 2, 1, 1 .                       1,  5, 11, 14, 12,  8, 5, 3, 2, 1, 1 .                   1,  6, 16, 25, 26, 20, 13, 8, 5, 3, 2, 1,1 .               1,  7, 22, 41, 51, 46, 33, 21,13, 8, 5, 3, 2,1,1 .           1,  8, 29, 63, 92, 97, 79, 54, 34,21,13, 8, 5, 3,2,1,1 .       1,  9, 37, 92,155,189,176,133, 88, 55,34,21,13, 8, 5,3,2,1,1 .    1,10, 46,129,247,344,365,309,221,143, 89,55,34,21,13, 8,5,3,2,1,1 . 1,11,56,175,376,591,709,674,530,364,232,144,89,55,34,21,13,8,5,3,2,1,1 . MATHEMATICA T[_, 1] = 1; T[n_, k_] /; k == 2*n-2 || k == 2*n-1 = 1; T[n_, k_] := T[n, k] = T[n-1, k-1] + T[n-1, k]; Table[T[n, k], {n, 1, 9}, {k, 1, 2*n-1}] // Flatten (* Jean-François Alcover, Oct 30 2017, after Reinhard Zumkeller *) PROG (Haskell) a162741 n k = a162741_tabf !! (n-1) !! (k-1) a162741_row n = a162741_tabf !! (n-1) a162741_tabf = iterate    (\row -> zipWith (+) ([0] ++ row ++ [0]) (row ++ [0, 1])) [1] -- Reinhard Zumkeller, Jul 16 2013 CROSSREFS Cf. A005408 (row length), A000225 (row sums), A000045 (central terms), A007318, A136431. Cf. A021113. - Mark Dols, Jul 18 2009 Some other Fibonacci-Pascal triangles: A027926, A036355, A037027, A074829, A105809, A109906, A111006, A114197, A228074. Sequence in context: A219365 A140751 A259922 * A104320 A242618 A180264 Adjacent sequences:  A162738 A162739 A162740 * A162742 A162743 A162744 KEYWORD nonn,tabf AUTHOR Mark Dols, Jul 12 2009, Jul 19 2009 STATUS approved

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Last modified November 15 07:25 EST 2018. Contains 317225 sequences. (Running on oeis4.)