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A136161 a(n) = 2*a(n-3)-a(n-6), starting a(0..5) = 0, 5, 2, 1, 3, 1. 0
0, 5, 2, 1, 3, 1, 2, 1, 0, 3, -1, -1, 4, -3, -2, 5, -5, -3, 6, -7, -4, 7, -9, -5, 8, -11, -6, 9, -13, -7, 10, -15, -8, 11, -17, -9, 12, -19, -10, 13, -21, -11, 14, -23, -12, 15, -25, -13, 16, -27, -14 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The intent is to show the triples (0,5,2), (1,3,1), (2,1,0), etc of the coefficients (k,5-2k,2-k), k=0,1,2,... that define recurrences a(n) = k*a(n-1) + (5-2k)*a(n-2) + (2-k)*a(n-3).

The first triple describes linear recurrences with "signature" 0, 5, 2 like A112685, A135138 etc.

The second triple describes linear recurrences with "signature" 1, 3, 1 like A097076. (See the OEIS index "recurrence, linear.." for more examples.)

LINKS

Table of n, a(n) for n=0..50.

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

FORMULA

G.f. -x*(-5-2*x-x^2+7*x^3+3*x^4) / ( (x-1)^2*(1+x+x^2)^2 ). - R. J. Mathar, Jul 06 2011

a(3n) = n. a(3n+1) = 5-2n. a(3n+3)=2-n.

MATHEMATICA

LinearRecurrence[{0, 0, 2, 0, 0, -1}, {0, 5, 2, 1, 3, 1}, 60] (* Harvey P. Dale, Aug 16 2012 *)

PROG

(PARI) Vec(-x*(-5-2*x-x^2+7*x^3+3*x^4) / ( (x-1)^2*(1+x+x^2)^2+O(x^99))) \\ Charles R Greathouse IV, Jul 06 2011

CROSSREFS

Cf. A135997, A137241.

Sequence in context: A038631 A158625 A133615 * A197383 A266455 A091505

Adjacent sequences:  A136158 A136159 A136160 * A136162 A136163 A136164

KEYWORD

sign,easy

AUTHOR

Paul Curtz, Mar 16 2008

STATUS

approved

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Last modified October 14 14:06 EDT 2019. Contains 328017 sequences. (Running on oeis4.)