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