A208245 Triangle read by rows: a(n,k) = a(n-2,k) + a(n-2,k-1).

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 3, 3, 2, 1, 1, 1, 3, 4, 3, 2, 1, 1, 1, 4, 6, 5, 3, 2, 1, 1, 1, 4, 7, 7, 5, 3, 2, 1, 1, 1, 5, 10, 11, 8, 5, 3, 2, 1, 1, 1, 5, 11, 14, 12, 8, 5, 3, 2, 1, 1, 1, 6, 15, 21, 19, 13, 8, 5, 3, 2, 1, 1, 1, 6, 16, 25, 26, 20, 13, 8, 5, 3, 2, 1, 1

Offset

1,8

Comments

Sum of terms in each row are given by sequence A052955.

Columns (at constant k) converge toward Fibonacci starting first from high value of k).

First seven rows are same as A008242. The odd numbered rows of this sequence equal the rows of A123736. Also it has some similarities to A162741.

Columns (constant k), prior to convergence to Fibonacci, appear as various other sequences (e.g. k = 4, is sequence A055803, with other columns in same referenced family).

Links

Reinhard Zumkeller, Rows n = 1..100 of triangle, flattened

Formula

a(n,k) = a(n-2,k) + a(n-2,k-1); if n=k or k=1 then a(n,k)=1; if n<k or n=0 then a(n,k)=0

Example

The first 13 rows are (as above) where n is the row index:
1
1, 1
1, 1, 1
1, 2, 1, 1
1, 2, 2, 1, 1
1, 3, 3, 2, 1, 1
1, 3, 4, 3, 2, 1, 1
1, 4, 6, 5, 3, 2, 1, 1
1, 4, 7, 7, 5, 3, 2, 1, 1
1, 5, 10, 11, 8, 5, 3, 2, 1, 1
1, 5, 11, 14, 12, 8, 5, 3, 2, 1, 1
1, 6, 15, 21, 19, 13, 8, 5, 3, 2, 1, 1
1, 6, 16, 25, 26, 20, 13, 8, 5, 3, 2, 1, 1,

Prog

(Haskell)
a208245 n k = a208245_tabl !! (n-1) !! (k-1)
a208245_row n = a208245_tabl !! (n-1)
a208245_tabl = map fst $ iterate f ([1], [1, 1]) where
   f (us, vs) = (vs, zipWith (+) ([0] ++ us ++ [0]) (us ++ [0, 1]))
-- Reinhard Zumkeller, Jul 28 2013

Crossrefs

Cf. A000045 (central terms).

Sequence in context: A215521 A008284 A114088 * A309049 A274190 A322596

Adjacent sequences: A208242 A208243 A208244 * A208246 A208247 A208248

Keyword

nonn,easy,tabl

Author

Richard R. Forberg, Apr 22 2013

Status

approved