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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

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

Programs

GAP

Filtered([0..250],n->n mod 8=2 or n mod 8=7); # Muniru A Asiru, Aug 06 2018

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 *)

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

Python

def A047524(n): return (n<<2)-1-(n&1) # Chai Wah Wu, Mar 30 2024

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

Extensions

More terms from Vincenzo Librandi, Aug 06 2010