OFFSET
-1,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = -1..1000
Robert Sedgewick, Analysis of shellsort and related algorithms, Fourth European Symposium on Algorithms, Barcelona, September, 1996.
Index entries for linear recurrences with constant coefficients, signature (7,-14,8).
FORMULA
a(n) = (1/2)*(A028401(n+4) + 1) for n > -1.
G.f.: (1+x-19*x^2+20*x^3)/(x*(1-x)*(1-2*x)*(1-4*x)). - Colin Barker, Mar 09 2012
a(n) = 7*a(n-1)-14*a(n-2)+8*a(n-3), for n>=3. - Wesley Ivan Hurt, Apr 26 2021
MATHEMATICA
CoefficientList[Series[x*(1+x-19*x^2+20*x^3)/(x*(1-x)*(1-2*x)*(1-4*x)), {x, 0, 30}], x] (* Vincenzo Librandi, Apr 24 2012 *)
PROG
(Magma) [1]cat[4^(n+1)+3*2^n+1:n in [0..30]]; // Vincenzo Librandi, Apr 24 2012
(PARI) a(n)=4^(n+1)+3*2^n+1 \\ Charles R Greathouse IV, Apr 24 2012
(Python)
def a(n): return 1 if n == -1 else (pow(4, n+1)+3*pow(2, n)+1)
print([a(n) for n in range(-1, 100)]) # Javier Rivera Romeu, Mar 05 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved