A047398 Numbers that are congruent to {3, 6} mod 8.

3, 6, 11, 14, 19, 22, 27, 30, 35, 38, 43, 46, 51, 54, 59, 62, 67, 70, 75, 78, 83, 86, 91, 94, 99, 102, 107, 110, 115, 118, 123, 126, 131, 134, 139, 142, 147, 150, 155, 158, 163, 166, 171, 174, 179, 182, 187, 190, 195, 198, 203, 206, 211, 214, 219, 222, 227, 230

Offset

1,1

Links

Table of n, a(n) for n=1..58.

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 05 2010

From R. J. Mathar, Dec 05 2011: (Start)

a(n) = 4*n - (3 + (-1)^n)/2.

G.f.: x*(3+3*x+2*x^2) / ( (1+x)*(x-1)^2 ). (End)

From Franck Maminirina Ramaharo, Aug 06 2018: (Start)

a(n) = a(n-1) + a(n-2) - a(n-3), n > 3.

a(n) = 4*n + (n mod 2) - 2.

a(n) = A047470(n) + 3.

a(2*n) = A017137(n-1).

a(2*n-1) = A017101(n-1).

E.g.f.: ((8*x - 3)*exp(x) - exp(-x) + 4)/2. (End)

Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(2)*Pi/16 + log(2)/8 - sqrt(2)*log(sqrt(2)+1)/8. - Amiram Eldar, Dec 18 2021

Maple

A047398:=n->4*n-(3+(-1)^n)/2: seq(A047398(n), n=1..100); # Wesley Ivan Hurt, Jan 30 2017

Mathematica

Flatten[# + {3, 6} & /@ (8 Range[0, 28])] (* Arkadiusz Wesolowski, Sep 25 2012 *)
LinearRecurrence[{1, 1, -1}, {3, 6, 11}, 60] (* Harvey P. Dale, Oct 26 2020 *)

Prog

(Maxima) makelist(4*n + mod(n, 2) - 2, n, 1, 100); /* Franck Maminirina Ramaharo, Aug 06 2018 */
(Python)
def A047398(n): return ((n<<2)|(n&1))-2 # Chai Wah Wu, Mar 30 2024

Crossrefs

Union of A017101 and A017137.

Cf. A047461, A047452, A047470, A047524, A047535, A047615, A047617.

Sequence in context: A026368 A246976 A189380 * A047924 A267519 A200182

Adjacent sequences: A047395 A047396 A047397 * A047399 A047400 A047401

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved