A374243 a(n) = ceiling(1/2 (n - 3 - ceiling((n - 3)/3))*ceiling((n - 3)/3)).

0, 0, 0, 0, 1, 1, 2, 3, 4, 6, 8, 9, 12, 14, 16, 20, 23, 25, 30, 33, 36, 42, 46, 49, 56, 60, 64, 72, 77, 81, 90, 95, 100, 110, 116, 121, 132, 138, 144, 156, 163, 169, 182, 189, 196, 210, 218, 225, 240, 248, 256, 272, 281, 289, 306, 315, 324, 342, 352, 361

Offset

1,7

Comments

a(n) is the rectilinear local crossing number of the complete graph K_n except for n = 8, 14.

Links

Table of n, a(n) for n=1..60.

B. M. Ábrego and S. Fernández-Merchant, The Rectilinear Local Crossing Number of K_n, J. Combin. Th. Ser. A, 151 (2017), 131-145.

Eric Weisstein's World of Mathematics, Complete Graph.

Eric Weisstein's World of Mathematics, Rectilinear Local Crossing Number.

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1,0,1,-1,0,-1,1).

Formula

G.f.: x^5*(-1-x^2-x^4-x^5)/((-1+x)^3*(1+x+x^2)^2*(1+x^3)).

a(n) = a(n-1) + a(n-3) - a(n-4) + a(n-6) - a(n-7) - a(n-9} + a(n-10).

Mathematica

Table[Ceiling[1/2 (n - 3 - Ceiling[(n - 3)/3]) Ceiling[(n - 3)/3]], {n, 20}]
Table[(89 - 9 (-1)^n + 6 n (-11 + 2 n) + 9 Cos[n Pi/3] + (19 - 6 n) Cos[2 n Pi/3] - 9 Sqrt[3] Sin[n Pi/3] + Sqrt[3] (-21 + 2 n) Sin[2 n Pi/3])/108, {n, 20}]
LinearRecurrence[{1, 0, 1, -1, 0, 1, -1, 0, -1, 1}, {0, 0, 0, 0, 1, 1, 2, 3, 4, 6}, 20]
CoefficientList[Series[x^4 (-1 - x^2 - x^4 - x^5)/((-1 + x)^3 (1 + x + x^2)^2 (1 + x^3)), {x, 0, 20}], x]

Crossrefs

Sequence in context: A113961 A116621 A036407 * A376154 A145807 A278962

Adjacent sequences: A374240 A374241 A374242 * A374244 A374245 A374246

Keyword

nonn,easy

Author

Eric W. Weisstein, Jul 01 2024

Status

approved