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A080871
a(n)*a(n+3) - a(n+1)*a(n+2) = 3, given a(0)=a(1)=1, a(2)=4.
6
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
0,3
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]
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 *)
CROSSREFS
Bisections are A001091 and A070997.
Sequence in context: A149088 A047004 A030689 * A358586 A102666 A123801
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 22 2003
STATUS
approved