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A208459 Triangle T_x = T(n,k) given by (0, 1/x, 1-1/x, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (x, 1/x-1, -1/x, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938, for x = 0. 0
1, 0, 0, 0, 1, 1, 0, 1, 0, -1, 0, 1, 0, 1, 2, 0, 1, 0, 2, 0, -3, 0, 1, 0, 3, -1, 0, 5, 0, 1, 0, 4, -2, 3, 2, -8, 0, 1, 0, 5, -3, 7, -2, -5, 13, 0, 1, 0, 6, -4, 12, -8, 2, 12, -21, 0, 1, 0, 7, -5, 18, -16, 15, 3, -25, 34 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,15

COMMENTS

Triangle T_x : T_1 = A103631, T_2 = A208343, T_3 = A208345.

LINKS

Table of n, a(n) for n=0..65.

FORMULA

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

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

Sum_{k, 0<=k<=n} T(n,k)*x^k = 12*A015548(n-1), 6*A085939(n-1), A106434(n), A000007(n), A000007(n), A077957(n), (-1)^n*A102901(n) for x = -4, -3, -2, -1, 0, 1, 2 respectively.

Sm_{k, 0<=k<=n} T(n,k)*x^(n-k) = A000007(n), A034834(n-1), A077957(n), A052533(n), (-1)^n*A086344(n) for x = -1, 0, 1, 2, 3 respectively.

EXAMPLE

Triangle begins :

1

0, 0

0, 1, 1

0, 1, 0, -1

0, 1, 0, 1, 2

0, 1, 0, 2, 0, -3

0, 1, 0, 3, -1, 0, 5

0, 1, 0, 4, -2, 3, 2, -8

0, 1, 0, 5, -3, 7, -2, -5, 13

0, 1, 0, 6, -4, 12, -8, 2, 12, -21

0, 1, 0, 7, -5, 18, -16, 15, 3, -25, 34

CROSSREFS

Cf. A103631, A208343, A208345, A000045 (Fibonacci)

Sequence in context: A230642 A053473 A322983 * A144764 A084929 A293575

Adjacent sequences:  A208456 A208457 A208458 * A208460 A208461 A208462

KEYWORD

easy,sign,tabl

AUTHOR

Philippe Deléham, Feb 27 2012

STATUS

approved

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Last modified August 13 19:30 EDT 2020. Contains 336451 sequences. (Running on oeis4.)