A193595 Augmentation of the Fibonacci triangle A058071. See Comments.
1, 1, 1, 2, 2, 3, 6, 8, 9, 13, 30, 42, 58, 56, 85, 240, 360, 480, 576, 533, 821, 3120, 4800, 6600, 7488, 8698, 7666, 12015, 65520, 102960, 141120, 165240, 178158, 200200, 171501, 271601, 2227680, 3538080, 4876560, 5670720, 6310590, 6513474
Offset: 0
Examples
First 5 rows of A193589: 1 1....1 2....2....3 6....8....9....13 30...42...58...56...85
Programs
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Mathematica
p[n_, k_] := Fibonacci[k + 1]*Fibonacci[n + 1 - k] Table[p[n, k], {n, 0, 5}, {k, 0, n}] (* A058071, a Fibonacci triangle *) 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, 10}]] (* A193595 *) Flatten[Table[v[n], {n, 0, 9}]]
Comments