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 A048878 Generalized Pellian with second term of 9. 4
 1, 9, 37, 157, 665, 2817, 11933, 50549, 214129, 907065, 3842389, 16276621, 68948873, 292072113, 1237237325, 5241021413, 22201322977, 94046313321, 398386576261, 1687592618365, 7148757049721, 30282620817249, 128279240318717, 543399582092117, 2301877568687185 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Harry J. Smith, Table of n, a(n) for n = 0..1584 Tanya Khovanova, Recursive Sequences. Index entries for linear recurrences with constant coefficients, signature (4,1). FORMULA a(n) = ( (7+sqrt(5))(2+sqrt(5))^n - (7-sqrt(5))(2-sqrt(5))^n )/2*sqrt(5). G.f.: (1+5*x)/(1-4*x-x^2). - Philippe Deléham, Nov 03 2008 a(n) = F(3*n+3) + F(3*n-2); F = A000045. - Yomna Bakr and Greg Dresden, May 25 2024 EXAMPLE a(n) = 4a(n-1) + a(n-2); a(0)=1, a(1)=9. MAPLE with(combinat): a:=n->5*fibonacci(n-1, 4)+fibonacci(n, 4): seq(a(n), n=1..16); # Zerinvary Lajos, Apr 04 2008 MATHEMATICA LinearRecurrence[{4, 1}, {1, 9}, 31] (* or *) CoefficientList[ Series[ (1+5x)/(1-4x-x^2), {x, 0, 30}], x] (* Harvey P. Dale, Jul 12 2011 *) PROG (PARI) { default(realprecision, 2000); for (n=0, 2000, a=round(((7+sqrt(5))*(2+sqrt(5))^n - (7-sqrt(5))*(2-sqrt(5))^n )/10*sqrt(5)); if (a > 10^(10^3 - 6), break); write("b048878.txt", n, " ", a); ); } \\ Harry J. Smith, May 31 2009 CROSSREFS Cf. A000045, A015448, A001077, A001076, A033887. Sequence in context: A257448 A288415 A026620 * A246315 A232250 A201441 Adjacent sequences: A048875 A048876 A048877 * A048879 A048880 A048881 KEYWORD nonn,easy,nice AUTHOR Barry E. Williams STATUS approved

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Last modified August 10 05:56 EDT 2024. Contains 375044 sequences. (Running on oeis4.)