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A046937 Triangle read by rows. Same rule as Aitken triangle (A011971) except T(0,0) = 1, T(1,0) = 2. 5
1, 2, 3, 3, 5, 8, 8, 11, 16, 24, 24, 32, 43, 59, 83, 83, 107, 139, 182, 241, 324, 324, 407, 514, 653, 835, 1076, 1400, 1400, 1724, 2131, 2645, 3298, 4133, 5209, 6609, 6609, 8009, 9733, 11864, 14509, 17807, 21940, 27149, 33758 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
EXAMPLE
Triangle starts:
[0] [ 1]
[1] [ 2, 3]
[2] [ 3, 5, 8]
[3] [ 8, 11, 16, 24]
[4] [ 24, 32, 43, 59, 83]
[5] [ 83, 107, 139, 182, 241, 324]
[6] [ 324, 407, 514, 653, 835, 1076, 1400]
[7] [1400, 1724, 2131, 2645, 3298, 4133, 5209, 6609]
[8] [6609, 8009, 9733, 11864, 14509, 17807, 21940, 27149, 33758]
MAPLE
# Compare the analogue algorithm for the Catalan triangle in A350584.
A046937Triangle := proc(len) local A, P, T, n; A := [2]; P := [1]; T := [[1]];
for n from 1 to len-1 do P := ListTools:-PartialSums([A[-1], op(P)]);
A := P; T := [op(T), P] od; T end:
A046937Triangle(9): ListTools:-Flatten(%); # Peter Luschny, Mar 27 2022
MATHEMATICA
a[0, 0] = 1; a[1, 0] = 2; 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, Jun 06 2013 *)
PROG
(Haskell)
a046937 n k = a046937_tabl !! n !! k
a046937_row n = a046937_tabl !! n
a046937_tabl = [1] : iterate (\row -> scanl (+) (last row) row) [2, 3]
-- Reinhard Zumkeller, Jan 13 2013
CROSSREFS
Borders give A038561.
Cf. A011971.
Sequence in context: A295352 A295606 A154690 * A247309 A069831 A017820
KEYWORD
tabl,easy,nice,nonn
AUTHOR
STATUS
approved

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Last modified May 30 06:57 EDT 2024. Contains 372961 sequences. (Running on oeis4.)