A080871 a(n)*a(n+3) - a(n+1)*a(n+2) = 3, given a(0)=a(1)=1, a(2)=4.

1, 1, 4, 7, 31, 55, 244, 433, 1921, 3409, 15124, 26839, 119071, 211303, 937444, 1663585, 7380481, 13097377, 58106404, 103115431, 457470751, 811826071, 3601659604, 6391493137, 28355806081, 50320119025, 223244789044

Offset: 0

Author

Paul D. Hanna, Feb 22 2003

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..2000
• Index entries for linear recurrences with constant coefficients, signature (0, 8, 0, -1).

Crossrefs

Cf. A001519, A079496, A080872, A080873, A080874, A080875.

Bisections are A001091 and A070997.

Programs

Mathematica

RecurrenceTable[{a[0]==a[1]==1,a[2]==4,a[n]==(3+a[n+1]a[n+2])/a[n+3]},a,{n,30}] (* Harvey P. Dale, Jun 08 2017 *)

Formula

a(n) = (3 + a(n-1)*a(n-2))/a(n-3) for n>2.

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

a(n+4) = 8*a(n+2)-a(n). [Richard Choulet, Dec 04 2008]

a(n) = (0.25 + sqrt(10)/20)*(sqrt(4 + sqrt(15)))^n + (0.25 + sqrt(10)/20)*(sqrt(4 - sqrt(15)))^n + ( - 1/20*10^(1/2) + 1/4)*( - sqrt(4 + sqrt(15)))^n + ( - 1/20*10^(1/2) + 1/4)*( - (sqrt(4 - sqrt(15))))^n. [Richard Choulet, Dec 06 2008]