OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
A. F. Horadam, Special Properties of the Sequence W(n){a,b; p,q}, Fib. Quart., Vol. 5, No. 5 (1967), pp. 424-434.
Index entries for linear recurrences with constant coefficients, signature (4,-4,0,1).
FORMULA
a(n) = 2a(n-1) + a(n-2) + (7n+1); a(0)=1, a(1)=10.
a(n) = ((((25/2)+17*sqrt(2)/2)(1+sqrt(2))^n - ((25/2)-17*sqrt(2)/2)(1-sqrt(2))^n)/2*sqrt(2)) - (7n+15)/2
(1/2) (4*Pell(n+2) - 3*Pell(n) - 7n - 15), with Pell(n) = A000129(n). - Ralf Stephan, May 15 2007
a(n) = 4*a(n-1) - 4*a(n-2) + a(n-4).
MATHEMATICA
LinearRecurrence[{4, -4, 0, 1}, {1, 10, 36, 104}, 40] (* Vincenzo Librandi, Jun 22 2012 *)
PROG
(Magma) I:=[1, 10, 36, 104]; [n le 4 select I[n] else 4*Self(n-1)-4*Self(n-2)+Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jun 22 2012
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Barry E. Williams, Jan 04 2000
STATUS
approved