OFFSET
1,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..500
Index entries for linear recurrences with constant coefficients, signature (6,-9,4).
FORMULA
From Rolf Pleisch, Aug 09 2009: (Start)
a(n) = 2(4^n-n) - 1;
a(n) = 2*A024037(n) - 1.
(End)
From Colin Barker, May 30 2020: (Start)
G.f.: x*(5 - 3*x + 4*x^2) / ((1 - x)^2*(1 - 4*x)).
a(n) = 6*a(n-1) - 9*a(n-2) + 4*a(n-3) for n>3.
(End)
MATHEMATICA
LinearRecurrence[{6, -9, 4}, {5, 27, 121}, 30] (* Harvey P. Dale, Jul 03 2021 *)
PROG
(PARI) for(n=1, 30, print1(-2*4^n*sum(i=1, 2*n+1, binomial(2*n+1, i)*bernfrac(i)/2^i), ", "))
(PARI) Vec(x*(5 - 3*x + 4*x^2) / ((1 - x)^2*(1 - 4*x)) + O(x^25)) \\ Colin Barker, May 30 2020
(Magma) [2*(4^n-n)-1: n in [1..30]]; // Vincenzo Librandi, Jul 02 2011
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, May 01 2002
STATUS
approved