A026323 Irregular triangular array T read by rows: T(0,0) = 1, T(0,1) = T(0,2) = 0; T(1,0) = T(1,1) = T(1,2) = 1, T(1,3) = 0; for n >= 2, T(n,0) = 1, T(n,1) = T(n-1,0) + T(n-1,1), T(n,k) = T(n-1,k-2) + T(n-1,k-1) + T(n-1,k) for k = 2,3,...,n+1 and T(n,n+2) = T(n-1,n) + T(n-1,n+1).

1, 0, 0, 1, 1, 1, 0, 1, 2, 3, 2, 1, 1, 3, 6, 7, 6, 3, 1, 4, 10, 16, 19, 16, 9, 1, 5, 15, 30, 45, 51, 44, 25, 1, 6, 21, 50, 90, 126, 140, 120, 69, 1, 7, 28, 77, 161, 266, 356, 386, 329, 189, 1, 8, 36, 112, 266, 504, 783, 1008, 1071, 904, 518, 1, 9, 45, 156, 414, 882, 1553, 2295, 2862, 2983, 2493

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• tabf
• easy

Examples

			First five rows:
  1  0  0
  1  1  1  0
  1  2  3  2  1
  1  3  6  7  6  3
  1  4 10 16 19 16  0
		

Crossrefs

Cf. A005774, A027907.

Programs

Mathematica

t[0, 0] = 1; t[0, 1] = 0; t[0, 2] = 0; t[1, 0] = 1; t[1, 1] = 1;
t[1, 2] = 1; t[1, 3] = 0;
t[n_, 0] := 1; t[n_, 1] := t[n - 1, 0] + t[n - 1, 1];
t[n_, k_] := t[n - 1, k - 2] + t[n - 1, k - 1] + t[n - 1, k] /; 2 <= k && k <= n + 1;
t[n_, k_] := t[n - 1, k - 2] + t[n - 1, k - 1] /; k == n + 2;
u = Table[t[n, k], {n, 0, 12}, {k, 0, n + 2}];
TableForm[u] (*A026323 array*)
v = Flatten[u] (*A026323 sequence*)
(* Clark Kimberling, Aug 21 2014 *)

Extensions

Beginning of sequence changed from 1,0,0,1,1,1,1,2,3,2,1,1,3,6,7,6,3 by N. J. A. Sloane (7/98).