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

0,2

Comments

See A350000 for background information.

Links

Table of n, a(n) for n=0..51.

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

Row 7 of the array in A350000.

Sequence in context: A206128 A333101 A206121 * A244696 A244697 A244698

Adjacent sequences: A349805 A349806 A349807 * A349809 A349810 A349811

Keyword

nonn

Author

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

Status

approved