cp's OEIS Frontend

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).

%I A026323 #15 Dec 28 2015 04:41:10
%S A026323 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,
%T A026323 51,44,25,1,6,21,50,90,126,140,120,69,1,7,28,77,161,266,356,386,329,
%U A026323 189,1,8,36,112,266,504,783,1008,1071,904,518,1,9,45,156,414,882,1553,2295,2862,2983,2493
%N 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).
%e A026323 First five rows:
%e A026323   1  0  0
%e A026323   1  1  1  0
%e A026323   1  2  3  2  1
%e A026323   1  3  6  7  6  3
%e A026323   1  4 10 16 19 16  0
%t A026323 t[0, 0] = 1; t[0, 1] = 0; t[0, 2] = 0; t[1, 0] = 1; t[1, 1] = 1;
%t A026323 t[1, 2] = 1; t[1, 3] = 0;
%t A026323 t[n_, 0] := 1; t[n_, 1] := t[n - 1, 0] + t[n - 1, 1];
%t A026323 t[n_, k_] := t[n - 1, k - 2] + t[n - 1, k - 1] + t[n - 1, k] /; 2 <= k && k <= n + 1;
%t A026323 t[n_, k_] := t[n - 1, k - 2] + t[n - 1, k - 1] /; k == n + 2;
%t A026323 u = Table[t[n, k], {n, 0, 12}, {k, 0, n + 2}];
%t A026323 TableForm[u] (*A026323 array*)
%t A026323 v = Flatten[u] (*A026323 sequence*)
%t A026323 (* _Clark Kimberling_, Aug 21 2014 *)
%Y A026323 Cf. A005774, A027907.
%K A026323 nonn,tabf,easy
%O A026323 1,9
%A A026323 _Clark Kimberling_
%E A026323 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).