A230435 Triangle by rows, A001047 convolved with A000079.

1, 2, 5, 4, 10, 19, 8, 20, 38, 65, 16, 40, 76, 130, 211, 32, 80, 152, 260, 422, 665, 64, 160, 304, 520, 844, 1330, 2059, 128, 320, 608, 1040, 1688, 2660, 4118, 6305, 256, 640, 1216, 2080, 3376, 5320, 8236, 12610, 19171

Offset: 0

Author

Christopher Tompkins, Nov 18 2013

Keywords

• nonn
• tabl

Comments

Generated from Running Total of each row of A036561.

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

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

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

Examples

			The start of the sequence as a triangle read by rows:
  1;
  2,  5;
  4,  10, 19;
  8,  20, 38,  65;
  16, 40, 76,  130, 211;
  32, 80, 152, 260, 422, 665;
  ...
		

Crossrefs

Cf. A000079, A001047, A036561, A066810.

Programs

Mathematica

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 *)

Formula

T(n,k) = Sum_{j=0..k} 3^j*2^(n-j). - Detlef Meya, Dec 20 2023

T(n,k) = 2^n*(3*(3/2)^k-2). - Alois P. Heinz, Dec 20 2023