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A137505 Inverse binomial transform of A007910. 2
1, 1, 0, 2, 0, 0, 4, -4, 4, 4, -12, 20, -12, -12, 52, -76, 52, 52, -204, 308, -204, -204, 820, -1228, 820, 820, -3276, 4916, -3276, -3276, 13108, -19660, 13108, 13108, -52428, 78644, -52428, -52428, 209716, -314572, 209716, 209716, -838860, 1258292, -838860, -838860, 3355444, -5033164, 3355444 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (-1,0,2).

FORMULA

Recurrence: a(n) = -a(n-1) + 2a(n-3), starting 1,1,0.

a(n) = 4/5 + (1/10 + 1/5*I)*(-1-I)^n + (1/10 - 1/5*I)*(-1+I)^n, with n>=0 and I=sqrt(-1) - Paolo P. Lava, Jun 03 2008

O.g.f.: (1+x)^2/((1-x)(1+2x+2x^2)). - R. J. Mathar, Jun 12 2008

a(4n) = a(4n+1) = (-1)^n*A109499(n). - Paul Curtz, Nov 01 2009

a(n) = (1/5) * (A137429(n-1) + 4) = A077973(n-2) + 2*A077973(n-1) + A077973(n). - Ralf Stephan, Aug 18 2013

MATHEMATICA

LinearRecurrence[{-1, 0, 2}, {1, 1, 0}, 50] (* Harvey P. Dale, Sep 17 2012 *)

CROSSREFS

Sequence in context: A137828 A264655 A264476 * A107498 A094295 A085969

Adjacent sequences:  A137502 A137503 A137504 * A137506 A137507 A137508

KEYWORD

sign

AUTHOR

Paul Curtz, Apr 23 2008

EXTENSIONS

More terms from R. J. Mathar, Jun 12 2008

STATUS

approved

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Last modified January 23 01:55 EST 2018. Contains 298093 sequences.