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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
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified February 21 18:44 EST 2020. Contains 332107 sequences. (Running on oeis4.)