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A131301 Regular triangle read by rows: T(n,k) = 3*binomial(floor((n+k)/2),k)-2.

%I A131301 #21 Feb 18 2022 22:33:24
%S A131301 1,1,1,1,1,1,1,4,1,1,1,4,7,1,1,1,7,7,10,1,1,1,7,16,10,13,1,1,1,10,16,
%T A131301 28,13,16,1,1,1,10,28,28,43,16,19,1,1,1,13,28,58,43,61,19,22,1,1,1,13,
%U A131301 43,58,103,61,82,22,25,1,1,1,16,43,103,103,166,82
%N A131301 Regular triangle read by rows: T(n,k) = 3*binomial(floor((n+k)/2),k)-2.
%C A131301 Row sums = A131300: (1, 2, 3, 7, 14, 27, 49, 86, ...). Reversed triangle = A131299.
%H A131301 Nathaniel Johnston, <a href="/A131301/b131301.txt">Rows 0..100, flattened</a>
%F A131301 3*A046854 - 2*A000012 as infinite lower triangular matrices (former name).
%F A131301 T(n,k) = 3*binomial(floor((n+k)/2),k)-2. - _Nathaniel Johnston_, Jun 29 2011
%e A131301 First few rows of the triangle:
%e A131301   1;
%e A131301   1,  1;
%e A131301   1,  1,  1;
%e A131301   1,  4,  1,  1;
%e A131301   1,  4,  7,  1,  1;
%e A131301   1,  7,  7, 10,  1,  1;
%e A131301   1,  7, 16, 10, 13,  1,  1;
%e A131301   ...
%p A131301 for n from 0 to 6 do seq(3*binomial(floor((n+k)/2),k)-2,k=0..n); od; # _Nathaniel Johnston_, Jun 29 2011
%t A131301 t[n_, k_] := 3 Binomial[Floor[(n + k)/2], k] - 2; Table[t[n, k], {n, 11}, {k, 0, n}] // Flatten
%t A131301 (* to view triangle: Table[t[n, k], {n, 5}, {k, 0, n}] // TableForm *) (* _Robert G. Wilson v_, Feb 28 2015 *)
%Y A131301 Cf. A046854, A000012, A131299, A131300.
%K A131301 nonn,easy,tabl
%O A131301 0,8
%A A131301 _Gary W. Adamson_, Jun 27 2007