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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Union of A008590 and A017077.

Programs

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

Mathematica

Riffle[#, # + 1] & [Range[0, 400, 8]] (* Paolo Xausa, Mar 11 2025 *)

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

Python

def A047393(n): return n-1<<2 if n&1 else (n<<2)-7 # Chai Wah Wu, Mar 11 2025

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

Extensions

More terms from James Sellers, Jun 20 2000