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!)
A202396 Triangle T(n,k), read by rows, given by (2, 1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (2, -1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. 2
1, 2, 2, 5, 8, 3, 13, 27, 19, 5, 34, 86, 86, 42, 8, 89, 265, 338, 234, 85, 13, 233, 798, 1227, 1084, 567, 166, 21, 610, 2362, 4230, 4510, 3038, 1286, 314, 34, 1597, 6898, 14058, 17474, 14284, 7814, 2774, 582, 55 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

T(n,n) = Fibonacci(n+2) = A000045(n+2).

LINKS

Table of n, a(n) for n=0..44.

FORMULA

T(n,k) = 3*T(n-1,k) + T(n-1,k-1) + T(n-2,k-2) - T(n-2,k) with T(0,0) = 1, T(1,0) = T(1,1) = 2 and T(n,k) = 0 if k<0 or if n<k.

G.f.: (1+(y-1)*x)/(1-(3+y)*x+(1-y^2)*x^2).

Sum_{k, 0<=k<=n} T(n,k)*x^k = A000007(n), A122367(n), A000302(n), A180035(n) for x = -1, 0, 1, 2 respectively.

Sum_{k, 0<=k<=n} T(n,k)*3^k = 2^n * A055099(n). - Philippe Deléham, Feb 05 2012

EXAMPLE

Triangle begins :

1

2, 2

5, 8, 3

13, 27, 19, 5

34, 86, 86, 42, 8

89, 265, 338, 234, 85, 13

CROSSREFS

Cf. A000045, A001519, A122367, A000302 (row sums), A202395

Sequence in context: A224791 A210637 A201972 * A210804 A087910 A327597

Adjacent sequences:  A202393 A202394 A202395 * A202397 A202398 A202399

KEYWORD

nonn,tabl

AUTHOR

Philippe Deléham, Dec 18 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 August 19 09:28 EDT 2022. Contains 356227 sequences. (Running on oeis4.)