OFFSET
1,1
COMMENTS
A195605 is a subsequence. - Bruno Berselli, Sep 21 2011
LINKS
Muniru A Asiru, Table of n, a(n) for n = 1..5000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
FORMULA
a(n) = 8*n - a(n-1) - 7, n > 1. - Vincenzo Librandi, Aug 06 2010
From R. J. Mathar, Mar 22 2011: (Start)
a(n) = 4*n - 3/2 + (-1)^n/2.
G.f.: x*(2+5*x+x^2) / ( (1+x)*(x-1)^2 ). (End)
From Franck Maminirina Ramaharo, Aug 06 2018: (Start)
a(n) = 4*n - (n mod 2) - 1.
a(n) = A047615(n) + 2.
a(2*n) = A004771(n-1).
a(2*n-1) = A017089(n-1).
E.g.f.: ((8*x - 3)*exp(x) + exp(-x) + 2)/2. (End)
a(n) = a(n-1) + a(n-2) - a(n-3). - Muniru A Asiru, Aug 06 2018
Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(2)+2)*Pi/16 - log(2)/8 - sqrt(2)*log(sqrt(2)+1)/8. - Amiram Eldar, Dec 11 2021
MAPLE
seq(coeff(series(x*(2+5*x+x^2)/((1+x)*(1-x)^2), x, n+1), x, n), n=1..60); # Muniru A Asiru, Aug 06 2018
MATHEMATICA
Select[Range[300], MemberQ[{2, 7}, Mod[#, 8]]&] (* or *)
LinearRecurrence[ {1, 1, -1}, {2, 7, 10}, 60] (* Harvey P. Dale, Nov 05 2017 *)
CoefficientList[ Series[(x^2 + 5x + 2)/((x - 1)^2 (x + 1)), {x, 0, 60}], x] (* Robert G. Wilson v, Aug 07 2018 *)
PROG
(Maxima) makelist(4*n - mod(n, 2) - 1, n, 1, 100); /* Franck Maminirina Ramaharo, Aug 06 2018 */
(PARI) is(n) = #setintersect([n%8], [2, 7]) > 0 \\ Felix Fröhlich, Aug 06 2018
(GAP) Filtered([0..250], n->n mod 8=2 or n mod 8=7); # Muniru A Asiru, Aug 06 2018
(Python)
def A047524(n): return (n<<2)-1-(n&1) # Chai Wah Wu, Mar 30 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Aug 06 2010
STATUS
approved