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A230435
Triangle by rows, A001047 convolved with A000079.
0
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, ...)
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
KEYWORD
nonn,tabl
AUTHOR
STATUS
approved