A047225 Numbers that are congruent to {0, 1} mod 6.

0, 1, 6, 7, 12, 13, 18, 19, 24, 25, 30, 31, 36, 37, 42, 43, 48, 49, 54, 55, 60, 61, 66, 67, 72, 73, 78, 79, 84, 85, 90, 91, 96, 97, 102, 103, 108, 109, 114, 115, 120, 121, 126, 127, 132, 133, 138, 139, 144, 145, 150

Offset

1,3

Comments

Also: 0 followed by partial sums of A010686. - R. J. Mathar, Feb 23 2008

Expansion of 1/(1 + x + x^2 + x^3 + x^4 + x^5) = 1 - x + x^6 - x^7 + x^12 - x^13 + ... and the exponents are the terms of this sequence. - Gary W. Adamson, Apr 04 2011

Numbers k such that floor(k/2) = 3*floor(k/6). - Bruno Berselli, Oct 05 2017

Links

David Lovler, Table of n, a(n) for n = 1..1000

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

Formula

From R. J. Mathar, Feb 23 2008: (Start)

O.g.f.: 1/(1+x) + 3/(-1+x)^2 + 4/(-1+x).

a(n) = a(n-2) + 6, n >= 2. (End)

a(n) = 6*n - a(n-1) - 11 for n>1, a(1)=0. - Vincenzo Librandi, Aug 05 2010

a(n+1) = Sum_{k>=0} A030308(n,k)*A082505(k+1). - Philippe Deléham, Oct 17 2011

Sum_{n>=2} (-1)^n/a(n) = sqrt(3)*Pi/12 + log(2)/3 + log(3)/4. - Amiram Eldar, Dec 13 2021

E.g.f.: 5 + (3*x - 4)*exp(x) - exp(-x). - David Lovler, Aug 25 2022

Maple

a[0]:=0:a[1]:=1:for n from 2 to 100 do a[n]:=a[n-2]+6 od: seq(a[n], n=0..50); # Zerinvary Lajos, Mar 16 2008

Mathematica

{#, #+1}&/@(6Range[0, 30])//Flatten (* or *) LinearRecurrence[{1, 1, -1}, {0, 1, 6}, 60] (* Harvey P. Dale, Aug 24 2019 *)

Prog

(PARI) forstep(n=0, 200, [1, 5], print1(n", ")) \\ Charles R Greathouse IV, Oct 17 2011

Crossrefs

Cf. A010686, A030308, A082505.

Sequence in context: A097354 A171153 A327313 * A374810 A374920 A191337

Adjacent sequences: A047222 A047223 A047224 * A047226 A047227 A047228

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Formula corrected by Paolo P. Lava, Oct 12 2010

Status

approved