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A046934 Same rule as Aitken triangle (A011971) except a(0,0)=1, a(1,0)=0.

%I A046934 #17 Mar 29 2022 08:37:24
%S A046934 1,0,1,1,1,2,2,3,4,6,6,8,11,15,21,21,27,35,46,61,82,82,103,130,165,
%T A046934 211,272,354,354,436,539,669,834,1045,1317,1671,1671,2025,2461,3000,
%U A046934 3669,4503,5548,6865,8536,8536,10207,12232,14693,17693,21362,25865,31413,38278,46814
%N A046934 Same rule as Aitken triangle (A011971) except a(0,0)=1, a(1,0)=0.
%C A046934 First differences of A046935 = this triangle seen as flattened list without the initial term. - _Reinhard Zumkeller_, Nov 10 2013
%H A046934 Reinhard Zumkeller, <a href="/A046934/b046934.txt">Rows n = 0..125 of triangle, flattened</a>
%e A046934 [0] [   1]
%e A046934 [1] [   0,     1]
%e A046934 [2] [   1,     1,     2]
%e A046934 [3] [   2,     3,     4,     6]
%e A046934 [4] [   6,     8,    11,    15,    21]
%e A046934 [5] [  21,    27,    35,    46,    61,    82]
%e A046934 [6] [  82,   103,   130,   165,   211,   272,   354]
%e A046934 [7] [ 354,   436,   539,   669,   834,  1045,  1317,  1671]
%e A046934 [8] [1671,  2025,  2461,  3000,  3669,  4503,  5548,  6865,  8536]
%e A046934 [9] [8536, 10207, 12232, 14693, 17693, 21362, 25865, 31413, 38278, 46814]
%p A046934 alias(PS = ListTools:-PartialSums):
%p A046934 A046934Triangle := proc(len) local a, k, P, T; a := 0; P := [1]; T := [];
%p A046934 for k from 1 to len  do T := [op(T), P]; P := PS([a, op(P)]); a := P[-1] od;
%p A046934 ListTools:-Flatten(T) end: A046934Triangle(10);  # _Peter Luschny_, Mar 29 2022
%t A046934 a[0, 0] = 1; a[1, 0] = 0; a[n_, 0] := a[n, 0] = a[n-1, n-1]; a[n_, k_] := a[n, k] = a[n, k-1] + a[n-1, k-1]; Table[a[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Oct 14 2013 *)
%o A046934 (Haskell)
%o A046934 a046934 n k = a046934_tabl !! n !! k
%o A046934 a046934_row n = a046934_tabl !! n
%o A046934 a046934_tabl = [1] : iterate (\row -> scanl (+) (last row) row) [0,1]
%o A046934 a046934_list = concat a046934_tabl
%o A046934 -- _Reinhard Zumkeller_, Nov 10 2013
%Y A046934 Borders give A032347 and A032346. Cf. A046935.
%K A046934 tabl,easy,nice,nonn
%O A046934 0,6
%A A046934 _N. J. A. Sloane_, _R. K. Guy_