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A270889 Integers n such that the circular graph C_n has a square size deficiency. 1
3, 6, 27, 150, 867, 5046, 29403, 171366, 998787, 5821350, 33929307, 197754486, 1152597603, 6717831126, 39154389147, 228208503750, 1330096633347, 7752371296326, 45184131144603, 263352415571286, 1534930362283107, 8946229758127350, 52142448186480987, 303908459360758566, 1771308307978070403 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Define the size deficiency of a graph G as the number of edges needed to complete G. If G is a cycle graph C_n, this sequence gives the values of n for which C_n has a size deficiency which is a perfect square.
LINKS
J. R. M. Antalan and I. F. Callano, On the Size Deficiency of Cycle Graphs and Some Integer Sequences, Asian Journal of Mathematics and Computer Research, 11 (3) (2016),192-200.
FORMULA
a(n+2) = 6*a(n+1) - a(n) - 6; a(0) = 3 , a(1) = 6.
G.f.: 3*(1-5*x+2*x^2)/((1-x)*(1-6*x+x^2)). - Joerg Arndt, Mar 25 2016
a(n) = 3 * A055997(n+1). - Joerg Arndt, Mar 25 2016
a(n) = 7*a(n-1)-7*a(n-2)+a(n-3) for n>2. - Colin Barker, Apr 03 2016
a(n) = 3*(2+(3-2*sqrt(2))^n+(3+2*sqrt(2))^n)/4. - Colin Barker, Apr 03 2016
MATHEMATICA
a[0] = 3; a[1] = 6; a[n_] := a[n] = 6 a[n - 1] - a[n - 2] - 6; Table[a@ n, {n, 0, 24}] (* Michael De Vlieger, Mar 25 2016 *)
LinearRecurrence[{7, -7, 1}, {3, 6, 27}, 30] (* Harvey P. Dale, Jan 23 2019 *)
PROG
(PARI) is(n)=issquare(n*(n-3)/2) \\ Charles R Greathouse IV, Mar 25 2016
(PARI) a(n)=([0, 1, 0; 0, 0, 1; 1, -7, 7]^n*[3; 6; 27])[1, 1] \\ Charles R Greathouse IV, Mar 25 2016
(PARI) Vec(3*(1-5*x+2*x^2)/((1-x)*(1-6*x+x^2)) + O(x^50)) \\ Colin Barker, Apr 03 2016
CROSSREFS
Sequence in context: A222625 A060170 A223143 * A097678 A251609 A366560
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified April 14 07:36 EDT 2024. Contains 371655 sequences. (Running on oeis4.)