OFFSET
1,1
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (4,1,-4).
FORMULA
If n is even, then 4^n + ... + 1 = (4^(n+1) - 1)/3 = (2^(n+1) - 1)(2^n+1) + 1)/3. - R. K. Guy, Nov 17 2003
a(n) = 4*a(n-1) + a(n-2) - 4*a(n-3). - Colin Barker, Apr 02 2012
G.f.: x*(6-3*x-4*x^2) / ((1-x)*(1+x)*(1-4*x)). - Colin Barker, Apr 02 2012
MATHEMATICA
LinearRecurrence[{4, 1, -4}, {6, 21, 86}, 50] (* Vincenzo Librandi, Jun 14 2015 *)
PROG
(PARI) trajpolypn(n1) = { for(x1=1, n1, y1 = polypn(4, x1); print1(y1", ") ) }
polypn(n, p) = { x=n; if(p%2, y=2, y=1); for(m=1, p, y=y+x^m; ); return(y) }
(PARI) Vec(x*(6-3*x-4*x^2)/((1-x)*(1+x)*(1-4*x)) + O(x^30)) \\ Colin Barker, Jun 13 2015
(Magma) I:=[6, 21, 86]; [n le 3 select I[n] else 4*Self(n-1)+Self(n-2)-4*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 14 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Cino Hilliard, Nov 17 2003
STATUS
approved