A193589 Augmentation of the Fibonacci triangle A193588. See Comments.
1, 1, 2, 1, 4, 7, 1, 6, 18, 31, 1, 8, 33, 90, 154, 1, 10, 52, 185, 481, 820, 1, 12, 75, 324, 1065, 2690, 4575, 1, 14, 102, 515, 2006, 6276, 15547, 26398, 1, 16, 133, 766, 3420, 12468, 37711, 92124, 156233, 1, 18, 168, 1085, 5439, 22412, 78030, 230277
Offset: 0
Examples
First 5 rows of A193588: 1 1....2 1....2....3 1....2....3....5 1....2....3....5....8 First 5 rows of A193589: 1 1....2 1....4....7 1....6....18...31 1....8....33...90...154
Programs
-
Mathematica
p[n_, k_] := Fibonacci[k + 2] Table[p[n, k], {n, 0, 5}, {k, 0, n}] (* A193588 *) m[n_] := Table[If[i <= j, p[n + 1 - i, j - i], 0], {i, n}, {j, n + 1}] TableForm[m[4]] w[0, 0] = 1; w[1, 0] = p[1, 0]; w[1, 1] = p[1, 1]; v[0] = w[0, 0]; v[1] = {w[1, 0], w[1, 1]}; v[n_] := v[n - 1].m[n] TableForm[Table[v[n], {n, 0, 6}]] (* A193589 *) Flatten[Table[v[n], {n, 0, 8}]]
Comments