A047225 - OEIS

%I #62 Feb 17 2024 10:33:44

%S 0,1,6,7,12,13,18,19,24,25,30,31,36,37,42,43,48,49,54,55,60,61,66,67,

%T 72,73,78,79,84,85,90,91,96,97,102,103,108,109,114,115,120,121,126,

%U 127,132,133,138,139,144,145,150

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

%C Also: 0 followed by partial sums of A010686. - _R. J. Mathar_, Feb 23 2008

%C 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

%C Numbers k such that floor(k/2) = 3*floor(k/6). - _Bruno Berselli_, Oct 05 2017

%H David Lovler, <a href="/A047225/b047225.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).

%F From _R. J. Mathar_, Feb 23 2008: (Start)

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

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

%F a(n) = 6*n - a(n-1) - 11 for n>1, a(1)=0. - _Vincenzo Librandi_, Aug 05 2010

%F a(n+1) = Sum_{k>=0} A030308(n,k)*A082505(k+1). - _Philippe Deléham_, Oct 17 2011

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

%F E.g.f.: 5 + (3*x - 4)*exp(x) - exp(-x). - _David Lovler_, Aug 25 2022

%p 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

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

%o (PARI) forstep(n=0,200,[1,5],print1(n", ")) \\ _Charles R Greathouse IV_, Oct 17 2011

%Y Cf. A010686, A030308, A082505.

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_

%E Formula corrected by _Paolo P. Lava_, Oct 12 2010