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 A193595 Augmentation of the Fibonacci triangle A058071.  See Comments. 2
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS For an introduction to the unary operation "augmentation" as applied to triangular arrays or sequences of polynomials, see A193091. Regarding A193595, (column 1)=A003266, (column 2)=A191994. LINKS EXAMPLE First 5 rows of A193589: 1 1....1 2....2....3 6....8....9....13 30...42...58...56...85 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}]] CROSSREFS Cf. A193091, A058071, A003266, A191994. Sequence in context: A159915 A007801 A275493 * A077871 A215450 A300352 Adjacent sequences:  A193592 A193593 A193594 * A193596 A193597 A193598 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Jul 31 2011 STATUS approved

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Last modified April 20 05:31 EDT 2021. Contains 343121 sequences. (Running on oeis4.)