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 A056123 a(n) = 3*a(n-1) - a(n-2) with a(0)=1, a(1)=11. 1
 1, 11, 32, 85, 223, 584, 1529, 4003, 10480, 27437, 71831, 188056, 492337, 1288955, 3374528, 8834629, 23129359, 60553448, 158530985, 415039507, 1086587536, 2844723101, 7447581767, 19498022200, 51046484833, 133641432299 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (3,-1). FORMULA a(n) = {11*[((3+sqrt(5))/2)^n - ((3-sqrt(5))/2)^n] - [((3+sqrt(5))/2)^(n-1) - ((3-sqrt(5))/2)^(n-1)]}/sqrt(5). G.f.: (1+8*x)/(1-3*x+x^2). a(n) = 6*Lucas(2n+1) - Fibonacci(2n+5). From G. C. Greubel, Jan 17 2020: (Start) a(n) = Fibonacci(2*n+2) + 8*Fibonacci(2*n). E.g.f.: exp(3*t/2)*( cosh(sqrt(5)*t/2) + (19/sqrt(5))*sinh(sqrt(5)*t/2) ). (End) MAPLE with(combinat); seq( fiboacci(2*n+2) +8*fibonacci(2*n), n=0..30); # G. C. Greubel, Jan 17 2020 MATHEMATICA Table[Fibonacci[2*n+2] +8*Fibonacci[2*n], {n, 0, 30}] (* G. C. Greubel, Jan 17 2020 *) PROG (PARI) vector(31, n, fibonacci(2*n) +8*fibonacci(2*n-2) ) \\ G. C. Greubel, Jan 17 2020 (MAGMA) [Fibonacci(2*n+2) +8*Fibonacci(2*n): n in [0..30]]; // G. C. Greubel, Jan 17 2020 (Sage) [fibonacci(2*n+2) +8*fibonacci(2*n) for n in (0..30)] # G. C. Greubel, Jan 17 2020 (GAP) List([0..30], n-> Fibonacci(2*n+2) +8*Fibonacci(2*n) ); # G. C. Greubel, Jan 17 2020 CROSSREFS Cf. A000032, A000045, A055850. Sequence in context: A007790 A195857 A048773 * A006655 A290640 A018956 Adjacent sequences:  A056120 A056121 A056122 * A056124 A056125 A056126 KEYWORD easy,nonn AUTHOR Barry E. Williams, Jul 06 2000 STATUS approved

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Last modified September 21 12:13 EDT 2020. Contains 337271 sequences. (Running on oeis4.)