A060522 Number of 4 X n grids of black and white cells, no 3 of same color vertically or horizontally contiguous.

10, 100, 378, 2030, 9484, 46746, 225654, 1098136, 5327258, 25875154, 125619088, 609970274, 2961628194, 14380186660, 69822244298, 339019686614, 1646096608476, 7992561729954, 38807580840854, 188428757462264, 914908750899146, 4442305123352810, 21569445781449640

Offset: 1

Author

Tom Womack (tom(AT)womack.net)

Keywords

• nonn

Comments

The 1 X n, 2 X n, 3 X n versions satisfied recurrence relations of degrees 2, 3, 4 respectively, but I have done quite a lot of LLL work and failed to find a degree-5 relation for this one.

Links

• R. H. Hardin, Table of n, a(n) for n = 1..212
• Sean A. Irvine, Java program (github)

Formula

Empirical: a(n)=3*a(n-1)+12*a(n-2)+a(n-3)-58*a(n-4)-115*a(n-5)+83*a(n-6)+312*a(n-7)+120*a(n-8)-336*a(n-9)-348*a(n-10)+420*a(n-11)+104*a(n-12)-194*a(n-13)+43*a(n-14)+35*a(n-15)-42*a(n-16)-3*a(n-17)+14*a(n-18)-a(n-19)-a(n-20) - R. H. Hardin, Jan 01 2012