A090850 - OEIS

%I #33 May 12 2020 07:49:29

%S 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,

%T 46,11,1,42,127,216,225,146,57,12,1,48,169,343,441,371,203,69,13,1,54,

%U 217,512,784,812,574,272,82,14,1,60,271,729,1296,1596,1386,846,354,96,15,1

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

%H Vincenzo Librandi, <a href="/A090850/b090850.txt">Rows n = 0..100, flattened</a>

%H Robert W. Donley Jr, <a href="https://arxiv.org/abs/1905.01525">Binomial arrays and generalized Vandermonde identities</a>, arXiv:1905.01525 [math.CO], 2019.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ClarksTriangle.html">Clark's Triangle</a>

%F c(n, k) = 6*binomial(n, k+1) + binomial(n-1, k-1). - _Max Alekseyev_, Nov 06 2005

%e Triangle starts

%e    0;

%e    6,  1;

%e   12,  7,  1;

%e   18, 19,  8,  1;

%e   ...

%t 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 *)

%o (Python)

%o from operator import add

%o f = 6

%o A090850_list = blist = [0]

%o for _ in range(20):

%o     blist = [blist[0]+f]+list(map(add,blist[:-1],blist[1:]))+[1]

%o     A090850_list.extend(blist) # _Chai Wah Wu_, Sep 18 2014

%Y Cf. A046902, A100206.

%K nonn,tabl

%O 0,2

%A _Eric W. Weisstein_, Dec 09 2003