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

%I A090850 #34 Feb 16 2025 08:32:52
%S A090850 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 A090850 46,11,1,42,127,216,225,146,57,12,1,48,169,343,441,371,203,69,13,1,54,
%U A090850 217,512,784,812,574,272,82,14,1,60,271,729,1296,1596,1386,846,354,96,15,1
%N A090850 Clark's triangle with f=6 read by row.
%H A090850 Vincenzo Librandi, <a href="/A090850/b090850.txt">Rows n = 0..100, flattened</a>
%H A090850 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 A090850 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ClarksTriangle.html">Clark's Triangle</a>
%F A090850 c(n, k) = 6*binomial(n, k+1) + binomial(n-1, k-1). - _Max Alekseyev_, Nov 06 2005
%e A090850 Triangle starts
%e A090850    0;
%e A090850    6,  1;
%e A090850   12,  7,  1;
%e A090850   18, 19,  8,  1;
%e A090850   ...
%t A090850 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 A090850 (Python)
%o A090850 from operator import add
%o A090850 f = 6
%o A090850 A090850_list = blist = [0]
%o A090850 for _ in range(20):
%o A090850     blist = [blist[0]+f]+list(map(add,blist[:-1],blist[1:]))+[1]
%o A090850     A090850_list.extend(blist) # _Chai Wah Wu_, Sep 18 2014
%Y A090850 Cf. A046902, A100206.
%K A090850 nonn,tabl
%O A090850 0,2
%A A090850 _Eric W. Weisstein_, Dec 09 2003