A047535 Numbers that are congruent to {4, 7} mod 8.

4, 7, 12, 15, 20, 23, 28, 31, 36, 39, 44, 47, 52, 55, 60, 63, 68, 71, 76, 79, 84, 87, 92, 95, 100, 103, 108, 111, 116, 119, 124, 127, 132, 135, 140, 143, 148, 151, 156, 159, 164, 167, 172, 175, 180, 183, 188, 191, 196, 199, 204, 207, 212, 215, 220, 223, 228, 231

Offset

1,1

Comments

Union of A004771 and A017113.

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) - 5 (with a(1)=4). - Vincenzo Librandi, Aug 06 2010

a(n) = 4*n -(1 + (-1)^n)/2. - Arkadiusz Wesolowski, Sep 18 2012

G.f.: x*(4+3*x+x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Jul 10 2015

From Franck Maminirina Ramaharo, Jul 22 2018: (Start)

a(n) = A047470(n) + 4.

E.g.f.: (2 - exp(-x) + (8*x - 1)*exp(x))/2. (End)

Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(2)+1)*Pi/16 - log(2)/4 - sqrt(2)*log(sqrt(2)+1)/8. - Amiram Eldar, Dec 11 2021

Maple

A047535:=n->4*n - (1 + (-1)^n)/2; seq(A047535(n), n=1..100); # Wesley Ivan Hurt, Feb 24 2014

Mathematica

Table[4n - (1 + (-1)^n)/2, {n, 100}] (* Wesley Ivan Hurt, Feb 24 2014 *)

Prog

(Maxima) makelist(4*n - (1 + (-1)^n)/2, n, 1, 100); /* Franck Maminirina Ramaharo, Jul 22 2018 */
(Python)
def A047535(n): return (n<<2)-(n&1^1) # Chai Wah Wu, Mar 30 2024

Crossrefs

Cf. A004771, A017113, A047398, A047461, A047452, A047470, A047524, A047615, A047617.

Sequence in context: A026360 A237514 A276888 * A310773 A310774 A182989

Adjacent sequences: A047532 A047533 A047534 * A047536 A047537 A047538

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved