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A080878
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a(n)*a(n+3) - a(n+1)*a(n+2) = 2^n, given a(0)=1, a(1)=1, a(2)=3.
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6
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1, 1, 3, 4, 14, 20, 72, 104, 376, 544, 1968, 2848, 10304, 14912, 53952, 78080, 282496, 408832, 1479168, 2140672, 7745024, 11208704, 40553472, 58689536, 212340736, 307302400, 1111830528, 1609056256, 5821620224, 8425127936, 30482399232
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| G.f.: (1+x-3x^2-2x^3)/(1-6x^2+4x^4). a(n)=6a(n-2)-4a(n-4). - Michael Somos, Mar 05 2003
G.f.: (-2*x^3 - 3*x^2 + x + 1)/(4*x^4 - 6*x^2 + 1)
a(n) = (1/20*10^(1/2) + 1/4)*(sqrt(3 + sqrt(5)))^n + (1/20*10^(1/2) + 1/4)*(sqrt(3 - sqrt(5)))^n + ( - 1/20*10^(1/2) + 1/4)*( - (sqrt(3 + sqrt(5))))^n + ( - 1/20*10^(1/2) + 1/4)*( - (sqrt(3 - sqrt(5))))^n [From Richard Choulet (richardchoulet(AT)yahoo.fr), Dec 07 2008]
a(n + 4) = 6*a(n + 2) - 4*a(n) [From Richard Choulet (richardchoulet(AT)yahoo.fr), Dec 06 2008]
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CROSSREFS
| Cf. A080876, A080877, A080879, A080880, A080881, A080882.
a(2n) = A080877(2n+1), a(2n+1) = A080877(2n+2)/2.
Sequence in context: A024863 A025107 A047182 * A110565 A057433 A006074
Adjacent sequences: A080875 A080876 A080877 * A080879 A080880 A080881
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Feb 22 2003
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