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.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A193998 Mirror of the triangle A193997. 2
1, 3, 2, 6, 8, 3, 11, 23, 18, 5, 19, 55, 66, 37, 8, 32, 120, 196, 167, 73, 13, 53, 246, 511, 587, 388, 139, 21, 87, 484, 1225, 1777, 1578, 853, 259, 34, 142, 924, 2765, 4857, 5428, 3933, 1799, 474, 55, 231, 1725, 5969, 12333, 16642, 15147, 9275, 3678 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
A193998 is obtained by reversing the rows of the triangle A193997.
LINKS
FORMULA
Write w(n,k) for the triangle at A193997. The triangle at A193998 is then given by w(n,n-k).
EXAMPLE
First six rows:
1
3....2
6....8.....3
11...23....18....5
19...55....66....37....8
32...120...196...167...73...13
MATHEMATICA
z = 11;
p[n_, x_] := Sum[Fibonacci[k + 1]*x^(n - k), {k, 0, n}];
q[n_, x_] := (x + 1)^n;
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}]] (* A193997 *)
TableForm[Table[h[n], {n, 0, z}]]
Flatten[Table[h[n], {n, -1, z}]] (* A193998 *)
CROSSREFS
Cf. A193997.
Sequence in context: A370665 A127717 A210236 * A209171 A368150 A348686
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 11 2011
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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 21 15:47 EDT 2024. Contains 372738 sequences. (Running on oeis4.)