A046936 - OEIS

%I #29 Jan 31 2018 21:51:47

%S 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 312,402,523,523,644,796,988,1232,1544,1946,2469,2469,2992,3636,4432,

%U 5420,6652,8196,10142,12611,12611,15080,18072,21708,26140

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

%H Reinhard Zumkeller, <a href="/A046936/b046936.txt">Rows n = 0..125 of triangle, flattened</a>

%H R. K. Guy, <a href="/A002186/a002186.pdf">Letters to N. J. A. Sloane, June-August 1968</a>

%H Don Knuth, <a href="/A040027/a040027.txt">Email to N. J. A. Sloane</a>, Jan 29 2018

%e Triangle starts:

%e 0,

%e 1, 1,

%e 1, 2, 3,

%e 3, 4, 6, 9,

%e 9, 12, 16, 22, 31,

%e 31, 40, 52, 68, 90, 121,

%e 121, 152, 192, 244, 312, 402, 523,

%e 523, 644, 796, 988, 1232, 1544, 1946, 2469,

%e 2469, 2992, 3636, 4432, 5420, 6652, 8196, 10142, 12611,

%e 12611, 15080, ...

%t 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 (Haskell)

%o a046936 n k = a046936_tabl !! n !! k

%o a046936_row n = a046936_tabl !! n

%o a046936_tabl = [0] : iterate (\row -> scanl (+) (last row) row) [1,1]

%o -- _Reinhard Zumkeller_, Jan 01 2014

%o (Python 3)

%o from itertools import accumulate

%o def A046936(): # Compare function Gould_diag in A121207.

%o     yield [0]

%o     accu = [1, 1]

%o     while True:

%o         yield accu

%o         accu = list(accumulate([accu[-1]] + accu))

%o g = A046936()

%o [next(g) for _ in range(9)] # _Peter Luschny_, Apr 25 2016

%Y Borders give A040027. Reading across rows gives A007604.

%Y Cf. A121207, A298804.

%K tabl,easy,nice,nonn

%O 0,5

%A _N. J. A. Sloane_, _R. K. Guy_