cp's OEIS Frontend

A026148 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).

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