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A047524
Numbers that are congruent to {2, 7} mod 8.
18
2, 7, 10, 15, 18, 23, 26, 31, 34, 39, 42, 47, 50, 55, 58, 63, 66, 71, 74, 79, 82, 87, 90, 95, 98, 103, 106, 111, 114, 119, 122, 127, 130, 135, 138, 143, 146, 151, 154, 159, 162, 167, 170, 175, 178, 183, 186, 191, 194, 199, 202, 207, 210, 215, 218, 223, 226, 231, 234
OFFSET
1,1
COMMENTS
A195605 is a subsequence. - Bruno Berselli, Sep 21 2011
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
KEYWORD
nonn,easy
EXTENSIONS
More terms from Vincenzo Librandi, Aug 06 2010
STATUS
approved