OFFSET
0,2
COMMENTS
See A350000 for background information.
LINKS
Scott R. Shannon, Illustration for a(1) = 50, the 7-gon after the first splitting.
Scott R. Shannon, Illustration for a(2) = 190, the 7-gon after the second splitting.
Scott R. Shannon, Illustration for a(3) = 400 (third generation).
Scott R. Shannon, Illustration for a(4) = 680 (fourth generation).
Scott R. Shannon, Illustration for a(5) = 1030 (fifth generation).
Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).
FORMULA
a(0)=1; for n>=1, a(n) = 35*k^2+35*k-20.
a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n >= 4, with a(0) = 1, a(1) = 50, a(2) = 190, a(3) = 400.
G.f.: (21*x^3-43*x^2-47*x-1)/(x-1)^3.
This sequence is most easily analyzed via the transition matrix M described in the Maple program.
MAPLE
with(LinearAlgebra):
M:=Matrix(5, 5, [ [1, 4, 10, 18, 35], [0, 0, 0, 6, 7], [0, 0, 1, 0, 7], [0, 0, 0, 0, 0], [0, 0, 0, 0, 1]]);
v:=Matrix(5, 1, [ [0], [0], [0], [0], [1]]); u:=Matrix(1, 5, [1, 1, 1, 1, 1]);
A349808:=n->(u.M^n.v)[1, 1];
CROSSREFS
KEYWORD
nonn
AUTHOR
Scott R. Shannon and N. J. A. Sloane, Dec 06 2021
STATUS
approved