This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A102105 a(n) = (19*5^n - 16*3^n + 1) / 4. 1
 1, 12, 83, 486, 2645, 13872, 71303, 362346, 1829225, 9198612, 46150523, 231225006, 1157542205, 5791962552, 28972567343, 144901100466, 724620293585, 3623445841692, 18118262329763, 90594411012726, 452981353155365, 2264934660052032, 11324756983085783 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Sum of the entries in the last row of the 3 X 3 matrix M^n, where M = {{1, 0, 0}, {2, 3, 0}, {3, 4, 5}}. Sum of the entries in the second row of M^n = A048473(n). LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (9,-23,15). FORMULA a(n) = 9*a(n-1) - 23*a(n-2) + 15*a(n-3), a(0)=1,a(1)=12,a(2)=83 (derived from the minimal polynomial of the matrix M). G.f.: (1 + 3*x - 2*x^2) / ((1 - x)*(1 - 3*x)*(1 - 5*x)). - Colin Barker, Mar 03 2017 EXAMPLE a(4) = 2645 = 9*486 - 23*83 + 15*12 = 9*a(3) - 23*a(2) + 15*a(1). a(4) = 2645 since M^4 * {1, 1, 1} = {1, 161, 2645}, where 161 = A048473(4). MAPLE with(linalg): M[1]:=matrix(3, 3, [1, 0, 0, 2, 3, 0, 3, 4, 5]): for n from 2 to 23 do M[n]:=multiply(M[1], M[n-1]) od: 1, seq(multiply(M[n], matrix(3, 1, [1, 1, 1]))[3, 1], n=1..23); PROG (PARI) Vec((1 + 3*x - 2*x^2) / ((1 - x)*(1 - 3*x)*(1 - 5*x)) + O(x^30)) \\ Colin Barker, Mar 03 2017 CROSSREFS Cf. A000326, A094727, A048473. Sequence in context: A290715 A175037 A252179 * A275743 A026949 A165127 Adjacent sequences:  A102102 A102103 A102104 * A102106 A102107 A102108 KEYWORD nonn,easy AUTHOR Gary W. Adamson, Dec 30 2004 EXTENSIONS Corrected by T. D. Noe, Nov 07 2006 Edited by N. J. A. Sloane, Dec 02 2006 New definition from Ralf Stephan, May 17 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 February 16 19:49 EST 2019. Contains 320167 sequences. (Running on oeis4.)