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