The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A123220 a(n)=the (1,1)-term of M^(n-1), where M=matrix(5,5, [3,-1,-1,-1,-1; 1,3,-1,-1,-1; 1,1,3,-1,-1; 1,1,1,3,-1; 1,1,1,1,3]). 0
 1, 3, 5, -9, -99, -297, 389, 8655, 46573, 122823, -120491, -3003393, -15885315, -40246281, 50400229, 1040606127, 5296630541, 12512952615, -22872751243, -368600380833, -1789336379619, -3926384911017, 9502037022725, 129579396089871, 602116408170541, 1219711972804743 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS FORMULA a(1) = 1; a(2) = 3; a(3) = 5; a(4) = -9; a(5) = -99; a(n) = 15a(n-1)-100a(n-2)+360a(n-3)-680a(n-4)+528a(n-5) for n>= 6. The minimal polynomial of M is x^5-15x^4+100x^3-360x^2+680x-528, the coefficients of which yield the coefficients of the recurrence relation. O.g.f.: -x*(1-12*x+60*x^2-144*x^3+136*x^4)/((3*x-1)*(176*x^4-168*x^3+64*x^2-12*x+1)). - R. J. Mathar, Dec 05 2007 MAPLE a[1]:=1:a[2]:=3:a[3]:=5:a[4]:=-9:a[5]:=-99: for n from 6 to 26 do a[n]:=15*a[n-1]-100*a[n-2]+360*a[n-3]-680*a[n-4]+528*a[n-5] od: seq(a[n], n=1..26); with(linalg): M[1]:=matrix(5, 5, [3, -1, -1, -1, -1, 1, 3, -1, -1, -1, 1, 1, 3, -1, -1, 1, 1, 1, 3, -1, 1, 1, 1, 1, 3]): for n from 2 to 25 do M[n]:=multiply(M[1], M[n-1]) od: 1, seq(M[n][1, 1], n=1..25); MATHEMATICA M = {{3, -1, -1, -1, -1}, {1, 3, -1, -1, -1}, {1, 1, 3, -1, -1}, {1, 1, 1, 3, -1}, {1, 1, 1, 1, 3}}; w[1] = {1, 0, 0, 0, 0}; w[n_] := w[n] = M.w[n - 1]; a = Table[w[n][[1]], {n, 1, 30}] CROSSREFS Cf. A000952, A074872, A085340. Sequence in context: A336144 A215440 A163550 * A098339 A121622 A188983 Adjacent sequences:  A123217 A123218 A123219 * A123221 A123222 A123223 KEYWORD sign AUTHOR Roger L. Bagula, Oct 05 2006 EXTENSIONS Edited by N. J. A. Sloane, Oct 15 2006 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 2 14:48 EST 2021. Contains 349445 sequences. (Running on oeis4.)