A202209 Triangle T(n,k), read by rows, given by (2, 1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

1, 2, 0, 5, 1, 0, 13, 5, 0, 0, 34, 19, 1, 0, 0, 89, 65, 8, 0, 0, 0, 233, 210, 42, 1, 0, 0, 0, 610, 654, 183, 11, 0, 0, 0, 0, 1597, 1985, 717, 74, 1, 0, 0, 0, 0, 4181, 5911, 2622, 394, 14, 0, 0, 0, 0, 0

Offset

0,2

Comments

Riordan array ((1-x)/(1-3x+x^2), x^2/(1-3x+x^2)) .

Links

Table of n, a(n) for n=0..54.

Formula

T(n,k) = 3*T(n-1,k) - T(n-2,k) + T(n-2,k-1).

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

Sum_{k, 0<=k<=n} T(n,k)*x^k = A057682(n+1), A000079(n), A122367(n), A025192(n), A052924(n), A104934(n), A202206(n), A122117(n), A197189(n) for x = -2, -1, 0, 1, 2, 3, 4, 5, 6 respectively.

T(n,0) = A122367(n) = A000045(2n+1).

Example

Triangle begins :
1
2, 0
5, 1, 0
13, 5, 0, 0
34, 19, 1, 0, 0
89, 65, 8, 0, 0, 0
233, 210, 42, 1, 0, 0, 0

Crossrefs

Cf. A000045, A000079, A001519, A001870, A001906, A126124, A202207 (antidiagonal sums)

Sequence in context: A261044 A117780 A155759 * A201730 A188449 A177267

Adjacent sequences: A202206 A202207 A202208 * A202210 A202211 A202212

Keyword

nonn,tabl

Author

Philippe Deléham, Dec 14 2011

Status

approved