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A046936 Same rule as Aitken triangle (A011971) except a(0,0)=0, a(1,0)=1.

%I A046936 #33 Mar 06 2025 15:27:31
%S A046936 0,1,1,1,2,3,3,4,6,9,9,12,16,22,31,31,40,52,68,90,121,121,152,192,244,
%T A046936 312,402,523,523,644,796,988,1232,1544,1946,2469,2469,2992,3636,4432,
%U A046936 5420,6652,8196,10142,12611,12611,15080,18072,21708,26140
%N A046936 Same rule as Aitken triangle (A011971) except a(0,0)=0, a(1,0)=1.
%H A046936 Reinhard Zumkeller, <a href="/A046936/b046936.txt">Rows n = 0..125 of triangle, flattened</a>
%H A046936 R. K. Guy, <a href="/A002186/a002186.pdf">Letters to N. J. A. Sloane, June-August 1968</a>
%H A046936 Don Knuth, <a href="/A040027/a040027.txt">Email to N. J. A. Sloane</a>, Jan 29 2018
%e A046936 Triangle starts:
%e A046936 0,
%e A046936 1, 1,
%e A046936 1, 2, 3,
%e A046936 3, 4, 6, 9,
%e A046936 9, 12, 16, 22, 31,
%e A046936 31, 40, 52, 68, 90, 121,
%e A046936 121, 152, 192, 244, 312, 402, 523,
%e A046936 523, 644, 796, 988, 1232, 1544, 1946, 2469,
%e A046936 2469, 2992, 3636, 4432, 5420, 6652, 8196, 10142, 12611,
%e A046936 12611, 15080, ...
%t A046936 a[0, 0] = 0; a[1, 0] = 1; 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_, Nov 15 2013 *)
%o A046936 (Haskell)
%o A046936 a046936 n k = a046936_tabl !! n !! k
%o A046936 a046936_row n = a046936_tabl !! n
%o A046936 a046936_tabl = [0] : iterate (\row -> scanl (+) (last row) row) [1,1]
%o A046936 -- _Reinhard Zumkeller_, Jan 01 2014
%o A046936 (Python)
%o A046936 from itertools import accumulate
%o A046936 def A046936(): # Compare function Gould_diag in A121207.
%o A046936     yield [0]
%o A046936     accu = [1, 1]
%o A046936     while True:
%o A046936         yield accu
%o A046936         accu = list(accumulate([accu[-1]] + accu))
%o A046936 g = A046936()
%o A046936 [next(g) for _ in range(9)] # _Peter Luschny_, Apr 25 2016
%Y A046936 Borders give A040027. Reading across rows gives A007604.
%Y A046936 Cf. A121207, A298804.
%K A046936 tabl,easy,nice,nonn
%O A046936 0,5
%A A046936 _N. J. A. Sloane_, _R. K. Guy_