cp's OEIS Frontend

A249095 Triangle read by rows: interleaving successive pairs of rows of Pascal's triangle.

%I A249095 #11 Dec 01 2014 02:51:58
%S A249095 1,1,1,1,1,1,2,1,1,1,1,3,2,3,1,1,1,1,4,3,6,3,4,1,1,1,1,5,4,10,6,10,4,
%T A249095 5,1,1,1,1,6,5,15,10,20,10,15,5,6,1,1,1,1,7,6,21,15,35,20,35,15,21,6,
%U A249095 7,1,1,1,1,8,7,28,21,56,35,70,35,56,21,28,7,8,1,1
%N A249095 Triangle read by rows: interleaving successive pairs of rows of Pascal's triangle.
%C A249095 Length of row n = 2*n+1;
%C A249095 T(n,2*k) = A007318(n,k), 0 <= k <= n;
%C A249095 T(n,2*k+1) = A007318(n-1,k-1), n > 0 and 0 <= k < n;
%C A249095 T(n,k) = T(n-1,k-2) + T(n-1,k), n > 0 and 2 <= k <= n-2;
%C A249095 T(n,2*k) = T(n-1,2*k) + T(n-1,2*(k-1)), k = 0..n;
%C A249095 T(n,2*k+1) = T(n-2,2*k), k = 0..n-1;
%C A249095 T(n,n) = A128014(n);
%C A249095 A105321(n) = number of odd terms in row n;
%C A249095 A249304(n) = number of even terms in row n;
%C A249095 T(n,k) mod 2 = A249133(n,k).
%H A249095 Reinhard Zumkeller, <a href="/A249095/b249095.txt">Rows n = 0..125 of triangle, flattened</a>
%H A249095 <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>
%F A249095 T(n,2*k) = T(n,2*k-1) + T(n,2*k+1), 0 < k < n.
%e A249095 The triangle begins:
%e A249095 .  0:                              1
%e A249095 .  1:                           1  1   1
%e A249095 .  2:                       1   1  2   1  1
%e A249095 .  3:                    1  1   3  2   3  1  1
%e A249095 .  4:                 1  1  4   3  6   3  4  1  1
%e A249095 .  5:              1  1  5  4  10  6  10  4  5  1  1
%e A249095 .  6:           1  1  6  5 15  10 20  10 15  5  6  1  1
%e A249095 .  7:        1  1  7  6 21 15  35 20  35 15 21  6  7  1  1
%e A249095 .  8:     1  1  8  7 28 21 56  35 70  35 56 21 28  7  8  1  1
%e A249095 .  9:  1  1  9  8 36 28 84 56 126 70 126 56 84 28 36  8  9  1  1 .
%t A249095 t[n_, k_] := If[n > 1 && 1 < k < 2*n - 1, If[EvenQ[k], t[n - 1, k] + t[n - 1, k - 2], t[n - 1, k - 1]], 1]; Grid[Table[t[n, k], {n, 0, 9}, {k, 0, 2*n}]] (* _L. Edson Jeffery_, Nov 30 2014 *)
%o A249095 (Haskell)
%o A249095 import Data.List (transpose)
%o A249095 a249095 n k = a249095_tabf !! n !! k
%o A249095 a249095_row n = a249095_tabf !! n
%o A249095 a249095_tabf = [1] : map (concat . transpose)
%o A249095    (zipWith ((. return) . (:)) (tail a007318_tabl) a007318_tabl)
%Y A249095 Cf. A005408 (row lengths), A128014 (central terms), A003945 (row sums), A249111 (partial sums per row), A007318 (Pascal).
%Y A249095 Cf. A105321, A249304, A249307, A249133.
%K A249095 nonn,tabf
%O A249095 0,7
%A A249095 _Reinhard Zumkeller_, Nov 14 2014