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A080873 a(n)*a(n+3) - a(n+1)*a(n+2) = 5, given a(0)=a(1)=1, a(2)=2. 5
1, 1, 2, 7, 19, 69, 188, 683, 1861, 6761, 18422, 66927, 182359, 662509, 1805168, 6558163, 17869321, 64919121, 176888042, 642633047, 1751011099, 6361411349, 17333222948, 62971480443, 171581218381, 623353393081, 1698478960862 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..2000

FORMULA

For n>1: a(2n-1)=3*a(2n-2)+2*a(2n-3)-a(2n-4); a(2n)=3*a(2n-1)-a(2n-2).

G.f.: (-3*x^3 - 8*x^2 + x + 1)/(x^4 - 10*x^2 + 1)

a(n+4) = 10*a(n+2)-a(n). [Richard Choulet, Dec 04 2008]

a(n) = (1/24*(3 + 3*3^(1/2)*2^(1/2) + 6*2^(1/2) + 2*3^(1/2))/(3^(1/2)*2^(1/2) + 2))*(sqrt(3) + sqrt(2))^n + (1/16*3^(1/2)*2^(1/2) + 1/8*2^(1/2) + 1/4 + 1/6*3^(1/2))*(sqrt(3) - sqrt(2))^n + (1/24*(3*3^(1/2)*2^(1/2) - 6*2^(1/2) + 3 - 2*3^(1/2))/(3^(1/2)*2^(1/2) + 2))*( - sqrt(3) - sqrt(2))^n + (1/16*3^(1/2)*2^(1/2) - 1/8*2^(1/2) + 1/4 - 1/6*3^(1/2))*( - sqrt(3) + sqrt(2))^n. [Richard Choulet, Dec 04 2008]

CROSSREFS

Cf. A080871, A080872, A080874, A080875.

Sequence in context: A318264 A164979 A243279 * A126162 A054423 A137990

Adjacent sequences:  A080870 A080871 A080872 * A080874 A080875 A080876

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Feb 22 2003

STATUS

approved

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Last modified January 27 14:39 EST 2020. Contains 331295 sequences. (Running on oeis4.)