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A208101 Triangle read by rows: T(n,0) = 1; for n > 0: T(n,1) = n, for n>1: T(n,n) = T(n-1,n-2); T(n,k) = T(n-2,k-1) + T(n-1,k) for k: 1 < k < n.

%I A208101 #22 Feb 03 2018 09:55:45
%S A208101 1,1,1,1,2,1,1,3,2,2,1,4,3,5,2,1,5,4,9,5,5,1,6,5,14,9,14,5,1,7,6,20,
%T A208101 14,28,14,14,1,8,7,27,20,48,28,42,14,1,9,8,35,27,75,48,90,42,42,1,10,
%U A208101 9,44,35,110,75,165,90,132,42,1,11,10,54,44,154,110
%N A208101 Triangle read by rows: T(n,0) = 1; for n > 0: T(n,1) = n, for n>1: T(n,n) = T(n-1,n-2); T(n,k) = T(n-2,k-1) + T(n-1,k) for k: 1 < k < n.
%C A208101 Another variant of Pascal's triangle, cf. A007318.
%H A208101 Reinhard Zumkeller, <a href="/A208101/b208101.txt">Rows n = 0..150 of triangle, flattened</a>
%H A208101 <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>
%e A208101 The triangle begins:
%e A208101 0:                    1
%e A208101 1:                  1   1
%e A208101 2:                1   2   1
%e A208101 3:              1   3   2   2
%e A208101 4:            1   4   3   5   2
%e A208101 5:          1   5   4   9   5   5
%e A208101 6:        1   6   5  14   9  14   5
%e A208101 7:      1   7   6  20  14  28  14  14
%e A208101 8:    1   8   7  27  20  48  28  42  14
%e A208101 9:  1   9   8  35  27  75  48  90  42  42
%t A208101 T[_, 0] = 1; T[n_, 1] := n; T[n_, n_] := T[n-1, n-2]; T[n_, k_] /; 1<k<n := T[n, k] = T[n-1, k] + T[n-1, k-2]; Table[T[n, k], {n, 0, 11}, {k, 0, n}]  // Flatten (* _Jean-François Alcover_, Feb 03 2018 *)
%o A208101 (Haskell)
%o A208101 a208101 n k = a208101_tabl !! n !! k
%o A208101 a208101_row n = a208101_tabl !! n
%o A208101 a208101_tabl =  iterate
%o A208101    (\row -> zipWith (+) ([0,1] ++ init row) (row ++ [0])) [1]
%Y A208101 Cf. A208976 (row sums), A101461 (row max), A208983 (central), A208355 (right edge), A074909.
%K A208101 nonn,tabl
%O A208101 0,5
%A A208101 _Reinhard Zumkeller_, Mar 04 2012