A047393 Numbers that are congruent to {0, 1} mod 8.

0, 1, 8, 9, 16, 17, 24, 25, 32, 33, 40, 41, 48, 49, 56, 57, 64, 65, 72, 73, 80, 81, 88, 89, 96, 97, 104, 105, 112, 113, 120, 121, 128, 129, 136, 137, 144, 145, 152, 153, 160, 161, 168, 169, 176, 177, 184, 185, 192, 193, 200, 201, 208, 209, 216, 217, 224, 225, 232

Offset

1,3

Comments

Numbers k such that floor(k/2) = 4*floor(k/8). - Bruno Berselli, Oct 05 2017

Links

David Lovler, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Formula

a(n) = 8*n - a(n-1) - 15 for n>1, a(1)=0. - Vincenzo Librandi, Aug 05 2010

From R. J. Mathar, Oct 08 2011: (Start)

a(n) = 4*n - 11/2 - 3*(-1)^n/2.

G.f.: x^2*(1+7*x) / ( (1+x)*(x-1)^2 ). (End)

a(n+1) = Sum_{k>=0} A030308(n,k)*A146541(k). - Philippe Deléham, Oct 17 2011

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

E.g.f.: ((8*x - 3)*exp(x) + 3*exp(-x))/2 = 4*x*exp(x) - 3*sinh(x). - David Lovler, Aug 02 2022

Maple

a[0]:=0:a[1]:=1:for n from 2 to 100 do a[n]:=a[n-2]+8 od: seq(a[n], n=0..58); # Zerinvary Lajos, Mar 16 2008

Prog

(PARI) forstep(n=0, 200, [1, 7], print1(n", ")) \\ Charles R Greathouse IV, Oct 17 2011
(PARI) a(n) = 4*n - 11/2 - 3*(-1)^n/2; \\ David Lovler, Jul 25 2022

Crossrefs

Union of A008590 and A017077.

Sequence in context: A265221 A286476 A265732 * A241263 A307417 A037371

Adjacent sequences: A047390 A047391 A047392 * A047394 A047395 A047396

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from James A. Sellers, Jun 20 2000

Status

approved