OFFSET
1,1
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
Index entries for linear recurrences with constant coefficients, signature (10,-37,59,-27,-25,21,5,-4,-1).
FORMULA
a(n) = 2*A378934(n). - Andrew Howroyd, Dec 12 2024
From Elmo R. Oliveira, Apr 03 2026: (Start)
a(n) = 10*a(n-1) - 37*a(n-2) + 59*a(n-3) - 27*a(n-4) - 25*a(n-5) + 21*a(n-6) + 5*a(n-7) - 4*a(n-8) - a(n-9) for n > 9.
G.f.: -2*x*(3*x^8 + 18*x^7 + 29*x^6 + 2*x^5 - 32*x^4 - 26*x^3 + 23*x^2 + 2*x - 3)/((1 - 3*x - x^2)*(1 - 2*x - x^2)^2*(1 - x)^3). (End)
EXAMPLE
Some solutions for n=4
...1.1.1.1...2.2.1.1...2.2.2.2...1.1.2.2...2.2.2.2...2.1.1.1...2.2.2.2
...1.2.1.1...2.1.1.1...1.2.1.2...2.1.1.2...1.1.2.1...2.2.1.1...2.2.2.2
...1.2.1.2...2.1.1.1...1.2.1.1...2.1.2.2...1.1.1.1...2.2.1.1...1.2.2.1
...2.2.2.2...1.1.1.1...1.1.1.1...2.2.2.2...1.1.1.1...2.1.1.1...1.1.1.1
------
...2.2.2.2...2.2.2.2...2.2.1.1...1.1.2.1...2.1.1.1...1.1.1.1...1.1.2.2
...2.1.1.1...1.1.1.2...1.2.2.1...1.1.2.1...2.1.2.2...1.2.1.2...1.1.1.1
...1.1.1.1...1.1.2.2...1.2.1.1...1.1.1.1...2.1.2.2...1.2.2.2...1.1.1.1
...1.1.1.1...2.2.2.2...1.1.1.1...1.1.1.1...2.2.2.2...1.1.2.2...1.1.1.1
MATHEMATICA
LinearRecurrence[{10, -37, 59, -27, -25, 21, 5, -4, -1}, {6, 56, 292, 1254, 4942, 18584, 67756, 241542, 846502}, 30] (* Paolo Xausa, Jan 09 2026 *)
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
R. H. Hardin, Oct 21 2009
EXTENSIONS
a(16) onwards from Andrew Howroyd, Dec 12 2024
STATUS
approved