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
KEYWORD
nonn,tabf
AUTHOR
Mark Dols, Jul 12 2009, Jul 19 2009
STATUS
approved