OFFSET
0,2
COMMENTS
Sum of n-th row of triangle of powers of 4: 1; 4 1 4; 16 4 1 4 16; 64 16 4 1 4 16 64; .... - Philippe Deléham, Feb 24 2014
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..170
Index entries for linear recurrences with constant coefficients, signature (5,-4).
FORMULA
a(n) = (8*4^n - 5)/3.
G.f.: (1+4*x)/((1-x)*(1-4*x)).
E.g.f.: (8*exp(4*x) - exp(x))/3.
a(0)=1, a(1)=9, a(n) = 5*a(n-1) - 4*a(n-2). - Harvey P. Dale, Oct 23 2011
a(n) = 4*a(n-1) + 5, a(0) = 1. - Philippe Deléham, Feb 24 2014
a(n+1) = 2^(2^n+1) + a(n), a(1)=1. - Ben Paul Thurston, Dec 27 2015
EXAMPLE
a(0) = 1;
a(1) = 4 + 1 + 4 = 9;
a(2) = 16 + 4 + 1 + 4 + 16 = 41;
a(3) = 64 + 16 + 4 + 1 + 4 + 16 + 64 = 169; etc. - Philippe Deléham, Feb 24 2014
MATHEMATICA
(8 4^Range[0, 30]-5)/3 (* or *) LinearRecurrence[{5, -4}, {1, 9}, 30] (* Harvey P. Dale, Oct 23 2011 *)
PROG
(Magma) [(8*4^n-5)/3: n in [0..40] ]; // Vincenzo Librandi, Apr 28 2011
(PARI) a(n)=(8*4^n-5)/3 \\ Charles R Greathouse IV, Oct 07 2015
(Python) print([8*4**n//3 - 1 for n in range(50)]) # Karl V. Keller, Jr., May 21 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 01 2003
STATUS
approved