OFFSET
0,3
COMMENTS
The {3,4,5} represents one of the few integer based triangular tilings of the plane by triangles.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,4,12).
FORMULA
p(x)=12 + 4 x + x^2 - x^3; a(n)=coefficient_expansion(-x^3*p(1/x)).
From Colin Barker, Jan 05 2018: (Start)
G.f.: 1 / (1 - x - 4*x^2 - 12*x^3).
a(n) = a(n-1) + 4*a(n-2) + 12*a(n-3) for n>2.
(End)
MATHEMATICA
f[x_] = 12 + 4 x + x^2 - x^3; g[x] = ExpandAll[ -x^3*f[1/x]]; a = Table[SeriesCoefficient[Series[1/g[x], {x, 0, 50}], n], {n, 0, 50}]
LinearRecurrence[{1, 4, 12}, {1, 1, 5}, 30] (* Harvey P. Dale, Jul 16 2023 *)
PROG
(PARI) Vec(1 / (1 - x - 4*x^2 - 12*x^3) + O(x^40)) \\ Colin Barker, Jan 05 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Nov 14 2008
STATUS
approved