A047452 Numbers that are congruent to {1, 6} mod 8.

1, 6, 9, 14, 17, 22, 25, 30, 33, 38, 41, 46, 49, 54, 57, 62, 65, 70, 73, 78, 81, 86, 89, 94, 97, 102, 105, 110, 113, 118, 121, 126, 129, 134, 137, 142, 145, 150, 153, 158, 161, 166, 169, 174, 177, 182, 185, 190

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Except for 1, numbers whose binary reflected Gray code (A014550) ends with 01. - Amiram Eldar, May 17 2021

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. A014550, A047398, A047461, A047470, A047524, A047535, A047615, A047617.

Programs

GAP

Filtered([0..250], n->n mod 8=1 or n mod 8=6); # Muniru A Asiru, Jul 24 2018

Maple

seq(coeff(series(factorial(n)*((4+exp(-x)+(8*x-5)*exp(x))/2), x,n+1),x,n),n=1..60); # Muniru A Asiru, Jul 24 2018

Mathematica

Table[(8 n - 5 + (-1)^n)/2, {n, 1, 100}] (* Franck Maminirina Ramaharo, Jul 23 2018 *)
CoefficientList[ Series[(2x^2 + 5x + 1)/((x - 1)^2 (x + 1)), {x, 0, 50}], x] (* or *)
LinearRecurrence[{1, 1, -1}, {1, 6, 9}, 51] (* Robert G. Wilson v, Jul 24 2018 *)

Maxima

makelist((8*n - 5 + (-1)^n)/2, n, 1, 100); /* Franck Maminirina Ramaharo, Jul 23 2018 */

Python

def A047452(n): return (n<<2)-2-(n&1) # Chai Wah Wu, Mar 30 2024

Formula

G.f.: x*(1+5*x+2*x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Dec 07 2011

E.g.f.: (4 + exp(-x) + (8*x - 5)*exp(x))/2. - Ilya Gutkovskiy, May 25 2016

a(n) = A047615(n) + 1. - Franck Maminirina Ramaharo, Jul 23 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