This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A133343 a(n)=2a(n-1)+13a(n-2) for n>1, a(0)=1, a(1)=1 . 6
 1, 1, 15, 43, 281, 1121, 5895, 26363, 129361, 601441, 2884575, 13587883, 64675241, 305992961, 1452764055, 6883436603, 32652805921, 154790287681, 734067052335, 3480407844523, 16503687369401, 78252676717601 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Binomial transform of A001023 (powers of 14), with interpolated zeros . a(n) is the number of compositions of n when there are 1 type of 1 and 14 types of other natural numbers. [From Milan Janjic, Aug 13 2010] LINKS Index entries for linear recurrences with constant coefficients, signature (2,13). FORMULA G.f.: (1-x)/(1-2x-13x^2). a(n)=Sum_{k, 0<=k<=n}A098158(n,k)*14^(n-k). - Philippe Deléham, Dec 26 2007 a(n)=(1/2)*[1-sqrt(14)]^n+(1/2)*[1+sqrt(14)]^n, n>=0 - Paolo P. Lava, Jun 10 2008 If p[1]=1, and p[i]=14, (i>1), and if A is Hessenberg matrix of order n defined by: A[i,j]=p[j-i+1], (i<=j), A[i,j]=-1, (i=j+1), and A[i,j]=0 otherwise. Then, for n>=1, a(n)=det A. [From Milan Janjic, Apr 29 2010] MATHEMATICA f[n_] := Simplify[((1 + Sqrt[14])^n + (1 - Sqrt[14])^n)/2]; Array[f, 25, 0] (* Or *) CoefficientList[Series[(1 + 13 x)/(1 - 2 x - 13 x^2), {x, 0, 23}], x] (* Or *) LinearRecurrence[{2, 13}, {1, 1}, 25] (* Or *) Table[ MatrixPower[{{1, 2}, {7, 1}}, n][[1, 1]], {n, 0, 30}]  (* Robert G. Wilson v, Sep 18 2013 *) PROG (PARI) Vec((1-x)/(1-2*x-13*x^2)+O(x^99)) \\ Charles R Greathouse IV, Jan 12 2012 CROSSREFS Sequence in context: A204734 A126369 A193647 * A027845 A201810 A292018 Adjacent sequences:  A133340 A133341 A133342 * A133344 A133345 A133346 KEYWORD nonn,easy AUTHOR Philippe Deléham, Dec 21 2007 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 14 22:42 EST 2019. Contains 329987 sequences. (Running on oeis4.)