login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A122789 The (1,4)-entry in the matrix M^n, where M is the 4 X 4 matrix {{0, -1, -1, 1}, {1, -1, 0, 0}, {0, 1, 1, 0}, {0, 0, 1, 1 }}. 1

%I

%S 0,1,1,0,0,1,2,2,2,3,5,7,9,12,17,24,33,45,62,86,119,164,226,312,431,

%T 595,821,1133,1564,2159,2980,4113,5677,7836,10816,14929,20606,28442,

%U 39258,54187,74793,103235,142493,196680,271473,374708,517201,713881,985354

%N The (1,4)-entry in the matrix M^n, where M is the 4 X 4 matrix {{0, -1, -1, 1}, {1, -1, 0, 0}, {0, 1, 1, 0}, {0, 0, 1, 1 }}.

%H Robert Israel, <a href="/A122789/b122789.txt">Table of n, a(n) for n = 0..3570</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 1).

%F a(n)=a(n-1)+a(n-4); a(0)=0, a(1)=a(2)=1, a(3)=0 (follows from the minimal polynomial x^4 -x^3-1 of the matrix M).

%F G.f.: x(1+x)(1-x)/(1-x-x^4). a(n+1)= A003269(n)-A003269(n-2). - _R. J. Mathar_, Nov 25 2008

%p a[0]:=0: a[1]:=1: a[2]:=1: a[3]:=0: for n from 4 to 50 do a[n]:=a[n-1]+a[n-4] od: seq(a[n],n=0..50);

%t M = {{0, -1, -1, 1}, {1, -1, 0, 0}, {0, 1, 1, 0}, {0, 0, 1, 1 }}; v[1] = {0, 0, 0, 1}; v[n_] := v[n] = M.v[n - 1]; a1 = Table[v[n][[1]], {n, 1, 50}]

%K nonn

%O 0,7

%A _Gary W. Adamson_ and _Roger L. Bagula_, Oct 20 2006

%E Edited by _N. J. A. Sloane_, Nov 07 2006

%E Offset corrected to match data by _Robert Israel_, Jul 11 2014

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 18 18:52 EDT 2019. Contains 324215 sequences. (Running on oeis4.)