This site is supported by donations to The OEIS Foundation.

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A201455 a(n) = 3*a(n-1) + 4*a(n-2) for n>1, a(0)=2, a(1)=3. 5
 2, 3, 17, 63, 257, 1023, 4097, 16383, 65537, 262143, 1048577, 4194303, 16777217, 67108863, 268435457, 1073741823, 4294967297, 17179869183, 68719476737, 274877906943, 1099511627777, 4398046511103, 17592186044417, 70368744177663, 281474976710657 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS This is the Lucas sequence V(3,-4). Inverse binomial transform of this sequence is A087451. LINKS Bruno Berselli, Table of n, a(n) for n = 0..200 Wikipedia, Lucas sequence: Specific names. Index entries for linear recurrences with constant coefficients, signature (3,4). FORMULA G.f.: (2-3*x)/((1+x)*(1-4*x)). a(n) = 4^n+(-1)^n. a(n) = A086341(A047524(n)) for n>0, a(0)=2. a(n) = [x^n] ( (1 + 3*x + sqrt(1 + 6*x + 25*x^2))/2 )^n for n >= 1. - Peter Bala, Jun 23 2015 MATHEMATICA RecurrenceTable[{a[n] == 3 a[n - 1] + 4 a[n - 2], a[0] == 2, a[1] == 3}, a[n], {n, 25}] PROG (MAGMA) [n le 1 select n+2 else 3*Self(n)+4*Self(n-1): n in [0..25]]; (Maxima) a[0]:2\$ a[1]:3\$ a[n]:=3*a[n-1]+4*a[n-2]\$ makelist(a[n], n, 0, 25); (PARI) Vec((2-3*x)/((1+x)*(1-4*x)) + O(x^30)) \\ Michel Marcus, Jun 26 2015 CROSSREFS Cf. for the same recurrence with initial values (i,i+1): A015521 (Lucas sequence U(3,-4); i=0), A122117 (i=1), A189738 (i=3). Cf. for similar closed form: A014551 (2^n+(-1)^n), A102345 (3^n+(-1)^n), A087404 (5^n+(-1)^n). Cf. A052539, A024036. Sequence in context: A042699 A078983 A235617 * A085874 A055739 A220703 Adjacent sequences:  A201452 A201453 A201454 * A201456 A201457 A201458 KEYWORD nonn,easy AUTHOR Bruno Berselli, Jan 09 2013 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.