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 A267652 a(n) = 4*a(n - 1) + 4*a(n - 2) for n>1, a(0)=2, a(1)=3. 0
 2, 3, 20, 92, 448, 2160, 10432, 50368, 243200, 1174272, 5669888, 27376640, 132186112, 638251008, 3081748480, 14879997952, 71846985728, 346907934720, 1675019681792, 8087710466048, 39050920591360, 188554524229632, 910421779283968, 4395905214054400, 21225307973353472, 102484852749631488 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Generalized Fibonacci sequence. LINKS Table of n, a(n) for n=0..25. Index entries for linear recurrences with constant coefficients, signature (4,4). FORMULA G.f.: (2 - 5*x)/(1 - 4*x - 4*x^2). a(n) = 2^(n-5/2)*((1+4*sqrt(2))*(1-sqrt(2))^n - (1-4*sqrt(2))*(1+sqrt(2))^n). Lim_{n -> infinity} a(n)/a(n - 1) = 2 + 2*sqrt(2) = 2*A014176 = 4.82842712... a(n) = 2*A057087(n)-5*A057087(n-1). - R. J. Mathar, Jun 07 2016 MATHEMATICA Table[2^(n - 5/2) ((1 + 4 Sqrt[2]) (1 - Sqrt[2])^n - (1 - 4 Sqrt[2]) (1 + Sqrt[2])^n), {n, 0, 25}] RecurrenceTable[{a[0] == 2, a[1] == 3, a[n] == 4 a[n - 1] + 4 a[n - 2]}, a, {n, 25}] (* Bruno Berselli, Jan 19 2016 *) LinearRecurrence[{4, 4}, {2, 3}, 20] (* Vincenzo Librandi, Jan 19 2016 *) PROG (PARI) Vec((2-5*x)/(1-4*x-4*x^2) + O(x^100)) \\ Altug Alkan, Jan 19 2016 CROSSREFS Cf. A057087, A084128. Sequence in context: A066166 A007113 A052804 * A258089 A165960 A125763 Adjacent sequences: A267649 A267650 A267651 * A267653 A267654 A267655 KEYWORD nonn,easy AUTHOR Ilya Gutkovskiy, Jan 19 2016 STATUS approved

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Last modified February 23 11:40 EST 2024. Contains 370283 sequences. (Running on oeis4.)