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!)
A216916 Triangle read by rows, T(n,k) for 0<=k<=n, generalizing A098742. 1
1, 1, 1, 3, 3, 1, 9, 12, 6, 1, 33, 51, 34, 10, 1, 135, 237, 193, 79, 15, 1, 609, 1188, 1132, 584, 160, 21, 1, 2985, 6381, 6920, 4268, 1510, 293, 28, 1, 15747, 36507, 44213, 31542, 13576, 3464, 497, 36, 1, 88761, 221400, 295314, 238261, 120206, 37839, 7231, 794 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Full concordance with A098742 would require two zero rows at the top of the triangle which we omitted for simplicity.

Matrix inverse is A137338. - Peter Luschny, Sep 21 2012

LINKS

Table of n, a(n) for n=0..52.

FORMULA

Recurrence: T(0,0)=1, T(0,k)=0 for k>0 and for n>=1 T(n,k) = T(n-1,k-1) + (k+1)*T(n-1,k) + (k+2)*T(n-1,k+1).

EXAMPLE

[0] [1]

[1] [1, 1]

[2] [3, 3, 1]

[3] [9, 12, 6, 1]

[4] [33, 51, 34, 10, 1]

[5] [135, 237, 193, 79, 15, 1]

[6] [609, 1188, 1132, 584, 160, 21, 1]

[7] [2985, 6381, 6920, 4268, 1510, 293, 28, 1]

[8] [15747, 36507, 44213, 31542, 13576, 3464, 497, 36, 1]

PROG

(Sage)

def A216916_triangle(dim):

    T = matrix(ZZ, dim, dim)

    for n in range(dim): T[n, n] = 1

    for n in (1..dim-1):

        for k in (0..n-1):

            T[n, k] = T[n-1, k-1]+(k+1)*T[n-1, k]+(k+2)*T[n-1, k+1]

    return T

A216916_triangle(9)

CROSSREFS

Sequence in context: A122919 A188513 A260301 * A157401 A143911 A185422

Adjacent sequences:  A216913 A216914 A216915 * A216917 A216918 A216919

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Sep 20 2012

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 July 13 04:31 EDT 2020. Contains 335673 sequences. (Running on oeis4.)