login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A058294 Successive rows of a triangle, the columns of which are generalized Fibonacci sequences S(j). 10
1, 1, 1, 1, 1, 2, 3, 2, 1, 1, 3, 7, 10, 7, 3, 1, 1, 4, 13, 30, 43, 30, 13, 4, 1, 1, 5, 21, 68, 157, 225, 157, 68, 21, 5, 1, 1, 6, 31, 130, 421, 972, 1393, 972, 421, 130, 31, 6, 1, 1, 7, 43, 222, 931, 3015, 6961, 9976, 6961, 3015, 931, 222, 43, 7, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

T(n,k)=A102473(n,k), k=1..n; T(n,k)=A102472(n,k-n+1), k=n..2*n-1; T(n,n)=A001040(n).  - Reinhard Zumkeller, Sep 14 2014

LINKS

Reinhard Zumkeller, >Rows n = 1..125 of table, flattened

Russell Walsmith, CL-Chemy Transforms Fibonacci-Type Sequences to Arrays

FORMULA

The j-th column S(j) is generated by a(n+1) = (n+j)*a(n) + a(n-1), a(0)=0, a(1)=1.

EXAMPLE

1;

1,1,1;

1,2,3,2,1;

1,3,7,10,7,3,1;

...

MATHEMATICA

t[n_, n_] = 1; t[n_, k_] := t[n, k] = If[n<k, 0, (n-1)*t[n-1, k] + t[n-2, k]]; row[n_] := With[{ro = Table[t[n, k], {k, 1, n}]}, Join[Reverse[ro], Rest[ro]]]; Array[row, 8] // Flatten (* Jean-Fran├žois Alcover, Oct 05 2016 *)

PROG

(Haskell)

a058294 n k = a058294_tabf !! (n-1) !! (k-1)

a058294_row n = a058294_tabf !! (n-1)

a058294_tabf = [1] : zipWith (++) xss (map (tail . reverse) xss)

               where xss = tail a102473_tabl

-- Reinhard Zumkeller, Sep 14 2014

CROSSREFS

A001040, A001053, A058307, A058308, A058309 are columns of this triangle.

Cf. A102472, A102473

Sequence in context: A026323 A017838 A181567 * A323834 A082868 A219539

Adjacent sequences:  A058291 A058292 A058293 * A058295 A058296 A058297

KEYWORD

nonn,tabf,nice,easy

AUTHOR

Russell Walsmith, Dec 07 2000

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 25 16:40 EDT 2020. Contains 334595 sequences. (Running on oeis4.)