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A208245
Triangle read by rows: a(n,k) = a(n-2,k) + a(n-2,k-1).
2
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
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
KEYWORD
nonn,easy,tabl
AUTHOR
Richard R. Forberg, Apr 22 2013
STATUS
approved