OFFSET
1,1
COMMENTS
Let M = [3,1,1,0; 1,3,0,1; 1,0,3,1; 0,1,1,3] be a 4 x 4 matrix. Then a(n) = [M^n]_ (0,1); n = 1,2,3,.... - Philippe Deléham, Aug 24 2020
With a(0) = 1, binomial transform of the sequence 1,2,6,20,72,272, ... (see A063376). - Philippe Deléham, Aug 24 2020
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..200
Index entries for linear recurrences with constant coefficients, signature (9,-23,15).
FORMULA
a(n) = (5^n+2*3^n+1)/4.
From Colin Barker, Dec 31 2013: (Start)
a(n) = 9*a(n-1)-23*a(n-2)+15*a(n-3).
G.f.: -x*(15*x^2-16*x+3) / ((x-1)*(3*x-1)*(5*x-1)). (End)
E.g.f.: exp(3*x)*(cosh(x))^2 - 1. - G. C. Greubel, Jan 31 2016
EXAMPLE
For n=2 the a(2)=11 numbers are 11, 33, 55, 57, 59, 75, 77, 79, 95, 97, 99.
MATHEMATICA
Table[(5^n + 2 3^n + 1)/4, {n, 1, 30}] (* Vincenzo Librandi, Dec 31 2013 *)
LinearRecurrence[{9, -23, 15}, {3, 11, 45}, 30] (* Harvey P. Dale, Dec 15 2014 *)
PROG
(PARI) a(n)=(5^n+2*3^n+1)/4; \\ Michel Marcus, Aug 22 2013
(Magma) [(5^n+2*3^n+1)/4: n in [1..30]]; // Vincenzo Librandi, Dec 31 2013
CROSSREFS
KEYWORD
base,easy,nonn
AUTHOR
Jake Foster, Oct 27 2008
EXTENSIONS
More terms from Colin Barker, Dec 31 2013
STATUS
approved