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3*A007318 - 2*A000012 as infinite lower triangular matrices.
12

%I #13 Feb 21 2022 00:26:16

%S 1,1,1,1,4,1,1,7,7,1,1,10,16,10,1,1,13,28,28,13,1,1,16,43,58,43,16,1,

%T 1,19,61,103,103,61,19,1,1,22,82,166,208,166,82,22,1,1,25,106,250,376,

%U 376,250,106,25,1,1,28,133,358,628,754,628,358,133,28,1

%N 3*A007318 - 2*A000012 as infinite lower triangular matrices.

%C Row sums = A097813: (1, 2, 6, 16, 38, 84, 178, ...).

%H G. C. Greubel, <a href="/A131060/b131060.txt">Rows n = 0..100 of triangle, flattened</a>

%F T(n,k) = 3*binomial(n,k) - 2. - _Roger L. Bagula_, Aug 20 2008

%e First few rows of the triangle:

%e 1;

%e 1, 1;

%e 1, 4, 1;

%e 1, 7, 7, 1;

%e 1, 10, 16, 10, 1;

%e 1, 13, 28, 28, 13, 1;

%e 1, 16, 43, 58, 43, 16, 1;

%e ...

%p A131060:= (n,k) -> 3*binomial(n, k)-2; seq(seq(A131060(n, k), k = 0..n), n = 0.. 10); # _G. C. Greubel_, Mar 12 2020

%t T[n_, k_] = 3*Binomial[n, k] -2; Table[T[n, k], {n,0,10}, {k,0,n}]//Flatten (* _Roger L. Bagula_, Aug 20 2008 *)

%o (Magma) [3*Binomial(n,k) -2: k in [0..n], n in [0..10]]; // _G. C. Greubel_, Mar 12 2020

%o (Sage) [[3*binomial(n,k) -2 for k in (0..n)] for n in (0..10)] # _G. C. Greubel_, Mar 12 2020

%Y Cf. A109128, A123203, A131061, A131063, A131064, A131065, A131066, A131067, A131068.

%K nonn,tabl

%O 0,5

%A _Gary W. Adamson_, Jun 13 2007

%E More terms from _Roger L. Bagula_, Aug 20 2008