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A046934
Same rule as Aitken triangle (A011971) except a(0,0)=1, a(1,0)=0.
8
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, 211, 272, 354, 354, 436, 539, 669, 834, 1045, 1317, 1671, 1671, 2025, 2461, 3000, 3669, 4503, 5548, 6865, 8536, 8536, 10207, 12232, 14693, 17693, 21362, 25865, 31413, 38278, 46814
OFFSET
0,6
COMMENTS
First differences of A046935 = this triangle seen as flattened list without the initial term. - Reinhard Zumkeller, Nov 10 2013
LINKS
EXAMPLE
[0] [ 1]
[1] [ 0, 1]
[2] [ 1, 1, 2]
[3] [ 2, 3, 4, 6]
[4] [ 6, 8, 11, 15, 21]
[5] [ 21, 27, 35, 46, 61, 82]
[6] [ 82, 103, 130, 165, 211, 272, 354]
[7] [ 354, 436, 539, 669, 834, 1045, 1317, 1671]
[8] [1671, 2025, 2461, 3000, 3669, 4503, 5548, 6865, 8536]
[9] [8536, 10207, 12232, 14693, 17693, 21362, 25865, 31413, 38278, 46814]
MAPLE
alias(PS = ListTools:-PartialSums):
A046934Triangle := proc(len) local a, k, P, T; a := 0; P := [1]; T := [];
for k from 1 to len do T := [op(T), P]; P := PS([a, op(P)]); a := P[-1] od;
ListTools:-Flatten(T) end: A046934Triangle(10); # Peter Luschny, Mar 29 2022
MATHEMATICA
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 *)
PROG
(Haskell)
a046934 n k = a046934_tabl !! n !! k
a046934_row n = a046934_tabl !! n
a046934_tabl = [1] : iterate (\row -> scanl (+) (last row) row) [0, 1]
a046934_list = concat a046934_tabl
-- Reinhard Zumkeller, Nov 10 2013
CROSSREFS
Borders give A032347 and A032346. Cf. A046935.
Sequence in context: A246778 A101344 A152048 * A093594 A008806 A356607
KEYWORD
tabl,easy,nice,nonn
STATUS
approved