This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A015537 Expansion of x/(1 - 5*x - 4*x^2). 13
 0, 1, 5, 29, 165, 941, 5365, 30589, 174405, 994381, 5669525, 32325149, 184303845, 1050819821, 5991314485, 34159851709, 194764516485, 1110461989261, 6331368012245, 36098688018269, 205818912140325, 1173489312774701, 6690722212434805 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS First differences give A122690(n) = {1, 4, 24, 136, 776, 4424, 25224, ...}. Partial sums of a(n) are {0, 1, 6, 35, 200, ...} = (A123270(n) - 1)/8. - Alexander Adamchuk, Nov 03 2006 For n >= 2, a(n) equals the permanent of the (n-1) X (n-1) tridiagonal matrix with 5's along the main diagonal, and 2's along the superdiagonal and the subdiagonal. - John M. Campbell, Jul 19 2011 Pisano period lengths:  1, 1, 8, 1, 4, 8, 48, 1, 24, 4, 40, 8, 42, 48, 8, 2, 72, 24, 360, 4, ... - R. J. Mathar, Aug 10 2012 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (5,4). FORMULA a(n) = 5*a(n-1) + 4*a(n-2). a(n) = Sum_{k=0..floor((n-1)/2)} C(n-k-1, k)*4^k*5^(n-2*k-1). - Paul Barry, Apr 23 2005 a(n) = Sum_{k=0..(n-1)} A122690(k). - Alexander Adamchuk, Nov 03 2006 a(n) = (1/41)*sqrt(41)*((5/2 + (1/2)*sqrt(41))^n - (5/2 - (1/2)*sqrt(41))^n), with n >= 0. - Paolo P. Lava, Jan 13 2009 MATHEMATICA Join[{a=0, b=1}, Table[c=5*b+4*a; a=b; b=c, {n, 100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 16 2011 *) LinearRecurrence[{5, 4}, {0, 1}, 30] (* Vincenzo Librandi, Nov 12 2012 *) PROG (Sage) [lucas_number1(n, 5, -4) for n in xrange(0, 22)] # Zerinvary Lajos, Apr 24 2009 (MAGMA) [n le 2 select n-1 else 5*Self(n-1)+4*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 12 2012 (PARI) x='x+O('x^30); concat([0], Vec(x/(1-5*x-4*x^2))) \\ G. C. Greubel, Jan 01 2018 CROSSREFS Cf. A001076, A006190, A007482, A015520, A015521, A015523, A015524, A015525, A015528, A015529, A015530, A015531, A015532, A015533, A015534, A015535, A015536, A015443, A015447, A030195, A053404, A057087, A083858, A085939, A090017, A091914, A099012, A122690, A123270, A180222, A180226. Sequence in context: A272940 A146178 A272751 * A182017 A291017 A141812 Adjacent sequences:  A015534 A015535 A015536 * A015538 A015539 A015540 KEYWORD nonn,easy,changed AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 19 09:50 EDT 2018. Contains 312774 sequences. (Running on oeis4.)