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%I #20 Jul 28 2013 12:20:07
%S 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,
%T 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,
%U 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
%N Triangle read by rows: a(n,k) = a(n-2,k) + a(n-2,k-1).
%C Sum of terms in each row are given by sequence A052955.
%C Columns (at constant k) converge toward Fibonacci starting first from high value of k).
%C 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.
%C 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).
%H Reinhard Zumkeller, <a href="/A208245/b208245.txt">Rows n = 1..100 of triangle, flattened</a>
%F 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
%e The first 13 rows are (as above) where n is the row index:
%e 1
%e 1, 1
%e 1, 1, 1
%e 1, 2, 1, 1
%e 1, 2, 2, 1, 1
%e 1, 3, 3, 2, 1, 1
%e 1, 3, 4, 3, 2, 1, 1
%e 1, 4, 6, 5, 3, 2, 1, 1
%e 1, 4, 7, 7, 5, 3, 2, 1, 1
%e 1, 5, 10, 11, 8, 5, 3, 2, 1, 1
%e 1, 5, 11, 14, 12, 8, 5, 3, 2, 1, 1
%e 1, 6, 15, 21, 19, 13, 8, 5, 3, 2, 1, 1
%e 1, 6, 16, 25, 26, 20, 13, 8, 5, 3, 2, 1, 1,
%o (Haskell)
%o a208245 n k = a208245_tabl !! (n-1) !! (k-1)
%o a208245_row n = a208245_tabl !! (n-1)
%o a208245_tabl = map fst $ iterate f ([1], [1, 1]) where
%o f (us, vs) = (vs, zipWith (+) ([0] ++ us ++ [0]) (us ++ [0, 1]))
%o -- _Reinhard Zumkeller_, Jul 28 2013
%Y Cf. A000045 (central terms).
%K nonn,easy,tabl
%O 1,8
%A _Richard R. Forberg_, Apr 22 2013
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