A349808 Number of cells in a regular 7-gon after n generations of mitosis.

1, 50, 190, 400, 680, 1030, 1450, 1940, 2500, 3130, 3830, 4600, 5440, 6350, 7330, 8380, 9500, 10690, 11950, 13280, 14680, 16150, 17690, 19300, 20980, 22730, 24550, 26440, 28400, 30430, 32530, 34700, 36940, 39250, 41630, 44080, 46600, 49190, 51850, 54580, 57380, 60250, 63190, 66200, 69280, 72430, 75650, 78940, 82300, 85730, 89230, 92800

Offset: 0

Author

Scott R. Shannon and N. J. A. Sloane, Dec 06 2021

Keywords

• nonn

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).

Crossrefs

Row 7 of the array in A350000.

Programs

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];

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.