OFFSET
0,2
COMMENTS
The first three terms are the same as A030186 because there are only monomers and dimers in boards with n<3.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Kathryn Haymaker and Sara Robertson, Counting Colorful Tilings of Rectangular Arrays, Journal of Integer Sequences, Vol. 20 (2017), Article 17.5.8, Corollary 2.
Index entries for linear recurrences with constant coefficients, signature (3,2,5,-2,0,-1).
FORMULA
a(n) = 3*a(n-1) + 2*a(n-2) + 5*a(n-3) - 2*a(n-4) - a(n-6).
G.f.: (1 - x - x^2 - x^3)/(1 - 3*x - 2*x^2 - 5*x^3 + 2*x^4 + x^6).
MAPLE
seq(coeff(series((1-x-x^2-x^3)/(1-3*x-2*x^2-5*x^3+2*x^4+x^6), x, n+1), x, n), n = 0..30); # G. C. Greubel, Oct 28 2019
MATHEMATICA
LinearRecurrence[{3, 2, 5, -2, 0, -1}, {1, 2, 7, 29, 109, 416}, 30] (* G. C. Greubel, Oct 28 2019 *)
PROG
(PARI) my(x='x+O('x^30)); Vec((1-x-x^2-x^3)/(1-3*x-2*x^2-5*x^3+ 2*x^4 +x^6)) \\ G. C. Greubel, Oct 28 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-x-x^2-x^3)/(1-3*x-2*x^2-5*x^3+2*x^4+x^6) )); // G. C. Greubel, Oct 28 2019
(Sage)
def A278815_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1-x-x^2-x^3)/(1-3*x-2*x^2-5*x^3+2*x^4+x^6) ).list()
A278815_list(30) # G. C. Greubel, Oct 28 2019
(GAP) a:=[1, 2, 7, 29, 109, 416];; for n in [7..30] do a[n]:=3*a[n-1]+2*a[n-2] +5*a[n-3]-2*a[n-4]-a[n-6]; od; a; # G. C. Greubel, Oct 28 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Kathryn Haymaker, Nov 28 2016
STATUS
approved