OFFSET
0,3
COMMENTS
a(n+1) = sum of n-th row of the triangle in A228074.
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-4,-1,2).
FORMULA
a(n) = A000079(n) - A000045(n) - 1 = A000225(n) - A000045(n) = A000079(n) - A001611(n) = A099036(n) - 1.
a(n) = 4*a(n-1)-4*a(n-2)-a(n-3)+2*a(n-4) for n>3. - Colin Barker, Mar 20 2015
G.f.: x^2*(3*x-2) / ((x-1)*(2*x-1)*(x^2+x-1)). - Colin Barker, Mar 20 2015
a(n) = (-1+2^n+(((1-sqrt(5))/2)^n-((1+sqrt(5))/2)^n)/sqrt(5)). - Colin Barker, Nov 02 2016
MATHEMATICA
Table[(2^n - Fibonacci[n] - 1), {n, 0, 40}] (* Vincenzo Librandi, Aug 16 2013 *)
PROG
(Haskell)
a228078 = subtract 1 . a099036
(Magma)
[2^n - Fibonacci(n) - 1: n in [0..40]]; // Vincenzo Librandi, Aug 16 2013
(PARI) concat([0, 0], Vec(x^2*(3*x-2)/((x-1)*(2*x-1)*(x^2+x-1)) + O(x^100))) \\ Colin Barker, Mar 20 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Aug 15 2013
STATUS
approved