OFFSET
1,2
COMMENTS
All even numbers m such that Integral_{x=0..2*Pi} Product_{i=1..m/2} cos(2*i*x) dx is nonzero. - William Boyles, Oct 12 2019
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
FORMULA
a(n) = 8*n - a(n-1) - 10 (with a(1)=0). - Vincenzo Librandi, Aug 06 2010
From R. J. Mathar, Oct 08 2011: (Start)
a(n) = 4*n - 3 + (-1)^n.
G.f.: 2*x^2*(3+x) / ( (1+x)*(x-1)^2 ). (End)
a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=6 and b(k)=2^(k+2) for k > 0. - Philippe Deléham, Oct 17 2011
a(n) = ceiling((8/3)*ceiling(3*n/2)). - Clark Kimberling, Jul 04 2012
Sum_{n>=2} (-1)^n/a(n) = 3*log(2)/8 - Pi/16. - Amiram Eldar, Dec 18 2021
E.g.f.: (4*x + 1)*exp(x) - exp(-x) = 4*x*exp(x) + 2*sinh(x). - David Lovler, Aug 02 2022
MATHEMATICA
Array[8 # + {0, 6} &, 29, 0] // Flatten (* or *)
Rest@ CoefficientList[Series[2 x^2*(3 + x)/((1 + x) (x - 1)^2), {x, 0, 58}], x] (* Michael De Vlieger, Nov 18 2019 *)
LinearRecurrence[{1, 1, -1}, {0, 6, 8}, 80] (* Harvey P. Dale, Apr 09 2022 *)
PROG
(PARI) forstep(n=0, 200, [6, 2], print1(n", ")) \\ Charles R Greathouse IV, Oct 17 2011
(PARI) a(n) = 4*n - 3 + (-1)^n; \\ David Lovler, Jul 25 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved