A090850 Clark's triangle with f=6 read by row.

0, 6, 1, 12, 7, 1, 18, 19, 8, 1, 24, 37, 27, 9, 1, 30, 61, 64, 36, 10, 1, 36, 91, 125, 100, 46, 11, 1, 42, 127, 216, 225, 146, 57, 12, 1, 48, 169, 343, 441, 371, 203, 69, 13, 1, 54, 217, 512, 784, 812, 574, 272, 82, 14, 1, 60, 271, 729, 1296, 1596, 1386, 846, 354, 96, 15, 1

Offset

0,2

Links

Vincenzo Librandi, Rows n = 0..100, flattened

Robert W. Donley Jr, Binomial arrays and generalized Vandermonde identities, arXiv:1905.01525 [math.CO], 2019.

Eric Weisstein's World of Mathematics, Clark's Triangle

Formula

c(n, k) = 6*binomial(n, k+1) + binomial(n-1, k-1). - Max Alekseyev, Nov 06 2005

Example

Triangle starts
   0;
   6,  1;
  12,  7,  1;
  18, 19,  8,  1;
  ...

Mathematica

Join[{0}, Rest[Flatten[Table[6*Binomial[n, k+1]+Binomial[n-1, k-1], {n, 0, 10}, {k, 0, n}]]]] (* Harvey P. Dale, Mar 29 2014 *)

Prog

(Python)
from operator import add
f = 6
A090850_list = blist = [0]
for _ in range(20):
    blist = [blist[0]+f]+list(map(add, blist[:-1], blist[1:]))+[1]
    A090850_list.extend(blist) # Chai Wah Wu, Sep 18 2014

Crossrefs

Cf. A046902, A100206.

Sequence in context: A162933 A304252 A229085 * A163945 A013613 A122508

Adjacent sequences: A090847 A090848 A090849 * A090851 A090852 A090853

Keyword

nonn,tabl

Author

Eric W. Weisstein, Dec 09 2003

Status

approved