A204565 - OEIS

A204565

Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..3 introduced in row major order.

8, 42, 256, 1682, 11448, 79162, 551216, 3849762, 26922088, 188375882, 1318394976, 9228056242, 64594267928, 452153498202, 3165055355536, 22155330093122, 155087138464968, 1085609452694122, 7599264619176896, 53194847685192402

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OFFSET

1,1

COMMENTS

Column 1 of A204572.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

Empirical: a(n) = 11*a(n-1) - 31*a(n-2) + 21*a(n-3).

Conjectures from Colin Barker, Jun 07 2018: (Start)

G.f.: 2*x*(4 - 23*x + 21*x^2) / ((1 - x)*(1 - 3*x)*(1 - 7*x)).

a(n) = 1/3 + 3^n + (2*7^n)/3.