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

1,2

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).

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

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 *)

Prog

(Maxima) makelist((8*n - 5 + (-1)^n)/2, n, 1, 100); /* Franck Maminirina Ramaharo, Jul 23 2018 */
(GAP) Filtered([0..250], n->n mod 8=1 or n mod 8=6); # Muniru A Asiru, Jul 24 2018
(Python)
def A047452(n): return (n<<2)-2-(n&1) # Chai Wah Wu, Mar 30 2024

Crossrefs

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

Sequence in context: A190443 A292151 A036992 * A315978 A315979 A315980

Adjacent sequences: A047449 A047450 A047451 * A047453 A047454 A047455

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved