A047524 Numbers that are congruent to {2, 7} mod 8.

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

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

Cf. A047398, A047461, A047452, A047470, A047535, A047615, A047617, A195605.

Sequence in context: A304799 A349499 A022886 * A190447 A190375 A066097

Adjacent sequences: A047521 A047522 A047523 * A047525 A047526 A047527

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Aug 06 2010

Status

approved