A080036 -id:A080036 - cp's OEIS frontend

A105206 Number of edges in a pancyclic graph on n+2 vertices with the fewest possible edges.

3, 5, 6, 8, 9, 10, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26

Offset: 3

John C. George (jgeorge(AT)gdn.edu), Walter D. Wallis (wdwallis(AT)siu.edu) and Alison Marr, Apr 12 2005

A graph on n vertices is said to be pancyclic if there are cycles of each length 3, 4, ... n in the graph.

			For n = 3 the answer is 3; each of the three vertices is connected to each other vertex, forming a 3-cycle. For n = 4 we find it takes five edges and for n = 5 it takes 6.

Different from A080036.

a(14)-a(22) by Alison Marr, Aug 22 2011

A080199 a(1)=1; for n>1, a(n)=a(n-1) - 3 if n is already in the sequence, a(n)=a(n-1) + 6 otherwise.

Original entry on oeis.org

1, 7, 13, 19, 25, 31, 28, 34, 40, 46, 52, 58, 55, 61, 67, 73, 79, 85, 82, 88, 94, 100, 106, 112, 109, 115, 121, 118, 124, 130, 127, 133, 139, 136, 142, 148, 154, 160, 166, 163, 169, 175, 181, 187, 193, 190, 196, 202, 208, 214, 220, 217, 223, 229

Offset: 1

N. J. A. Sloane, Mar 20 2003

nonn

B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence (math.NT/0305308)

Cf. A080455-A080458, A080036, A080037.

a[1] = 1;
a[n_] := a[n] = If[MemberQ[Array[a, n-1], n], a[n-1]-3, a[n-1]+6];
Array[a, 54] (* Jean-François Alcover, Feb 13 2019 *)

a(n) = 3*n*(1 + 1/log_3(n)) + o(n).

A080460 a(1) = 2; for n > 1, a(n) = a(n-1) if n is already in the sequence, a(n) = a(n-1) + 4 otherwise.

Original entry on oeis.org

2, 2, 6, 10, 14, 14, 18, 22, 26, 26, 30, 34, 38, 38, 42, 46, 50, 50, 54, 58, 62, 62, 66, 70, 74, 74, 78, 82, 86, 86, 90, 94, 98, 98, 102, 106, 110, 110, 114, 118, 122, 122, 126, 130, 134, 134, 138, 142, 146, 146, 150, 154, 158, 158, 162, 166, 170, 170

Offset: 1

N. J. A. Sloane and Benoit Cloitre, Mar 22 2003

B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, arXiv:math/0305308 [math.NT], 2003.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Cf. A080455, A080456, A080457, A080458, A080036, A080037.

LinearRecurrence[{1, 0, 0, 1, -1}, {2, 2, 6, 10, 14}, 58] (* Jean-François Alcover, Jan 07 2019 *)

a(n)=4*n - (n-2)\4*4 - 6 \\ Charles R Greathouse IV, Jul 17 2016

a(n) = 2 + 4*(n - 2 - floor((n - 2)/4)).
From Chai Wah Wu, Jul 17 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n > 5.
G.f.: 2*x*(x^4 + 2*x^3 + 2*x^2 + 1)/(x^5 - x^4 - x + 1). (End)
From Ilya Gutkovskiy, Jul 17 2016: (Start)
E.g.f.: 2 + (3*x - 2)*sinh(x) + 3*(x - 1)*cosh(x) + sin(x) + cos(x).
a(n) = (6*n - (-1)^n + 2*sqrt(2)*sin(Pi*n/2 + Pi/4) - 5)/2. (End)

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A105206 Number of edges in a pancyclic graph on n+2 vertices with the fewest possible edges.

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A080199 a(1)=1; for n>1, a(n)=a(n-1) - 3 if n is already in the sequence, a(n)=a(n-1) + 6 otherwise.

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A080460 a(1) = 2; for n > 1, a(n) = a(n-1) if n is already in the sequence, a(n) = a(n-1) + 4 otherwise.

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