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