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Triangle by rows, A001047 convolved with A000079.
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%I #28 Dec 20 2023 09:59:49

%S 1,2,5,4,10,19,8,20,38,65,16,40,76,130,211,32,80,152,260,422,665,64,

%T 160,304,520,844,1330,2059,128,320,608,1040,1688,2660,4118,6305,256,

%U 640,1216,2080,3376,5320,8236,12610,19171

%N Triangle by rows, A001047 convolved with A000079.

%C Generated from Running Total of each row of A036561.

%C Left edge is A000079 (offset 0): (1, 2, 4, 8, 16, 32, 64, ...)

%C Right edge is A001047 (offset 1): (1, 5, 19, 65, 211, 665, ...)

%C Row sums are A066810 (offset 2): (1, 7, 33, 131, 473, 1611, ...)

%F T(n,k) = Sum_{j=0..k} 3^j*2^(n-j). - _Detlef Meya_, Dec 20 2023

%F T(n,k) = 2^n*(3*(3/2)^k-2). - _Alois P. Heinz_, Dec 20 2023

%e The start of the sequence as a triangle read by rows:

%e 1;

%e 2, 5;

%e 4, 10, 19;

%e 8, 20, 38, 65;

%e 16, 40, 76, 130, 211;

%e 32, 80, 152, 260, 422, 665;

%e ...

%t T[n_,k_]:=Sum[3^j*2^(n-j),{j,0,k}];Flatten[Table[T[n,k],{n,0,8},{k,0,n}]] (* _Detlef Meya_, Dec 20 2023 *)

%Y Cf. A000079, A001047, A036561, A066810.

%K nonn,tabl

%O 0,2

%A _Christopher Tompkins_, Nov 18 2013