Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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_