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

Author

Richard R. Forberg, Apr 22 2013

Keywords

• nonn
• easy
• tabl

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).

Examples

			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,
		

Links

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

Crossrefs

Cf. A000045 (central terms).

Programs

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

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

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