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A047225 Numbers that are congruent to {0, 1} mod 6. 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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..51.

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) = -1 + (-1)^(n-1) + 3*(n-1). - Paolo P. Lava, Oct 06 2008

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

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

Sequence in context: A097354 A171153 A327313 * A191337 A276089 A037364

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

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Last modified October 16 02:52 EDT 2019. Contains 328038 sequences. (Running on oeis4.)