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.

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

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