The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A193999 Mirror of the triangle A094585. 2
 1, 3, 2, 6, 5, 3, 11, 10, 8, 5, 19, 18, 16, 13, 8, 32, 31, 29, 26, 21, 13, 53, 52, 50, 47, 42, 34, 21, 87, 86, 84, 81, 76, 68, 55, 34, 142, 141, 139, 136, 131, 123, 110, 89, 55, 231, 230, 228, 225, 220, 212, 199, 178, 144, 89, 375, 374, 372, 369, 364, 356, 343 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A193999 is obtained by reversing the rows of the triangle A094585. LINKS Muniru A Asiru, Table of n, a(n) for n = 1..11325 FORMULA Write w(n,k) for the triangle at A094585. The triangle at A094585 is then given by w(n,n-k). T(n,k) = Fibonacci(n+3) - Fibonacci(k+2) for n > 0 and 1 <= k <= n. - Rigoberto Florez, Oct 03 2019 EXAMPLE First six rows: 1; 3, 2; 6, 5, 3; 11, 10, 8, 5; 19, 18, 16, 13, 8; 32, 31, 29, 26, 21, 13; MATHEMATICA z = 11; p[n_, x_] := Sum[Fibonacci[k + 1]*x^(n - k), {k, 0, n}]; q[n_, x_] := x*q[n - 1, x] + 1; q[0, n_] := 1; p1[n_, k_] := Coefficient[p[n, x], x^k]; p1[n_, 0] := p[n, x] /. x -> 0; d[n_, x_] := Sum[p1[n, k]*q[n - 1 - k, x], {k, 0, n - 1}] h[n_] := CoefficientList[d[n, x], {x}] TableForm[Table[Reverse[h[n]], {n, 0, z}]] Flatten[Table[Reverse[h[n]], {n, -1, z}]] (* A094585 *) TableForm[Table[h[n], {n, 0, z}]] Flatten[Table[h[n], {n, -1, z}]] (* A193999 *) (* alternate program *) Table[Fibonacci[n+3]-Fibonacci[k+2], {n, 1, 10}, {k, 1, n}] //TableForm (* Rigoberto Florez, Oct 03 2019 *) PROG (GAP) Flat(List([1..11], n->Reversed(List([1..n], k->Fibonacci(n+3)-Fibonacci(n-k+3))))); # Muniru A Asiru, Apr 28 2019 CROSSREFS Cf. A094585. Sequence in context: A297878 A234922 A049777 * A210971 A212000 A058401 Adjacent sequences: A193996 A193997 A193998 * A194000 A194001 A194002 KEYWORD nonn AUTHOR Clark Kimberling, Aug 11 2011 EXTENSIONS Offset 1 from Muniru A Asiru, Apr 29 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 23 15:19 EDT 2024. Contains 372763 sequences. (Running on oeis4.)