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

0,2

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, ...)

Links

Table of n, a(n) for n=0..44.

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

Example

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;
  ...

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 *)

Crossrefs

Cf. A000079, A001047, A036561, A066810.

Sequence in context: A356875 A114393 A241256 * A180338 A232646 A100710

Adjacent sequences: A230432 A230433 A230434 * A230436 A230437 A230438

Keyword

nonn,tabl

Author

Christopher Tompkins, Nov 18 2013

Status

approved