A087328 Independence numbers for KT_3 knight on hexagonal board.

1, 3, 4, 4, 9, 12, 15, 16, 22, 27, 31, 36, 43, 51, 58, 64, 75, 83, 93, 100, 112, 123, 133, 144, 157, 171, 184, 196, 213, 227, 243, 256, 274, 291, 307, 324, 343, 363, 382, 400, 423, 443, 465, 484, 508, 531, 553, 576, 601, 627, 652, 676, 705, 731, 759, 784, 814

Offset: 1

Author

N. J. A. Sloane, Oct 21 2003

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• J.-P. Bode and H. Harborth, Independence for knights on hexagon and triangle boards, Discrete Math., 272 (2003), 27-35.
• Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1,0,-1,2,0,-2,1).

Crossrefs

Cf. A087327, A087329.

Programs

PARI

Vec(x*(1+x-2*x^2-2*x^3+6*x^4-x^5-4*x^6+x^7+3*x^8-x^9+x^11-2*x^12+2*x^14-x^15)/((1-x)^3*(1+x)*(1+x^2)*(1-x^2+x^4)) + O(x^100)) \\ Colin Barker, Feb 02 2016

Formula

a(n) = ceiling(n^2/4) if n == 0, 1, 4, 8, 11 (mod 12), ceiling(n^2/4) + 1 if n == 3, 9 (mod 12) and ceiling(n^2/4) + 2 if n == 2, 5, 6, 7, 10 (mod 12) and n != 6.

G.f.: x*(1+x-2*x^2-2*x^3+6*x^4-x^5-4*x^6+x^7+3*x^8-x^9+x^11-2*x^12+2*x^14-x^15) / ((1-x)^3*(1+x)*(1+x^2)*(1-x^2+x^4)). - Colin Barker, Feb 02 2016

Extensions

More terms from David Wasserman, May 06 2005