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
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).
Programs
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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