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%I #19 Aug 12 2022 09:26:49
%S 1,1,1,1,1,2,1,1,1,2,4,4,4,2,1,3,7,10,12,10,6,1,4,11,20,29,32,28,16,1,
%T 5,16,35,60,81,89,76,44,1,6,22,56,111,176,230,246,209,120,1,7,29,84,
%U 189,343,517,652,685,575,329,1,8,37,120,302,616,1049,1512,1854,1912,1589,904,1,9,46,165
%N Irregular triangular array T read by rows: T(n,0) = 1 for i >= 0, T(1,1) = 1,T(2,1) = 1, T(2,2) = 2, T(2,3) = 1, T(2,4) = 1 and for n >= 3, T(n,1) = n-1, T(n,k) = T(n-1,k-2) + T(n-1,k-1) + T(n-1,k) for k=2,...,n+1, and T(n, k+2) = T(n-1, k) + T(n-1, k+1).
%H Clark Kimberling, <a href="/A026148/b026148.txt">Table of n, a(n) for n = 1..5000</a>
%e First 7 rows:
%e 1
%e 1 1
%e 1 1 2 1 1
%e 1 2 4 4 4 2
%e 1 3 7 10 12 10 6
%e 1 4 11 20 29 32 28 16
%e 1 5 16 35 60 81 89 76 44
%t z = 12; t[n_, 0] = 1; t[1, 1] = 1; t[2, 2] = 2; t[2, 3] = 1; t[2, 4] = 1; t[n_, 1] := t[n, 1] = n - 1; t[n_, k_] := t[n, k] = Which[2 <= k <= n + 1, t[n - 1, k - 2] + t[n - 1, k - 1] + t[n - 1, k], k == n + 2, t[n - 1, k - 2] + t[n - 1, k - 1]]; u = Join[{{1}}, {{1, 1}}, Table[t[n, k], {n, 2, z}, {k, 0, n + 2}]]; TableForm[u] (* A026148 array *)
%t Flatten[u] (* A026148 sequence *) (* _Clark Kimberling_, Aug 28 2014 *)
%K nonn,tabf
%O 1,6
%A _Clark Kimberling_
%E Definition clarified and Example by _Clark Kimberling_, Aug 28 2014
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