OFFSET
1,2
COMMENTS
From J. Volkmar Schmidt, Oct 25 2023 (Start)
Proof of formula for a(n) follows proof scheme from David A. Corneth for A186864.
Distribution matrix of surrounding rectangles for 4-step walks is:
[0 0 0 2]
[0 24 80 28]
[0 80 80 20]
[2 28 20 4] (End)
LINKS
J. Volkmar Schmidt, Table of n, a(n) for n = 1..50
Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).
FORMULA
a(n) = 368*n^2 - 1308*n + 1108 = 4*(92*(n-1)*(n-3) + 41*n + 1) for n > 2.
G.f.: 4*x^2*(6 + 106*x + 87*x^2 - 15*x^3)/(1-x)^3. - Colin Barker, Jan 22 2012
EXAMPLE
Some solutions for 3 X 3:
0 3 0 0 2 0 0 0 1 1 0 0 0 0 0 0 4 3 4 0 0
0 2 4 0 3 1 0 0 2 4 2 0 0 1 4 0 2 1 1 3 0
0 1 0 0 0 4 4 3 0 3 0 0 0 3 2 0 0 0 2 0 0
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Feb 27 2011
EXTENSIONS
a(34)-a(39) from J. Volkmar Schmidt, Sep 03 2023
STATUS
approved