A358598 Number of genetic relatives of a person M in a genealogical tree extending back n generations and where everyone has 4 children down to the generation of M.

1, 6, 40, 300, 2356, 18756, 149860, 1198500, 9587236, 76696356, 613567780, 4908536100, 39268276516, 314146187556, 2513169451300, 20105355512100, 160842843900196, 1286742750808356, 10293942005680420, 82351536043870500, 658812288347818276, 5270498306776254756

Offset: 0

Author

Hans Braxmeier, Nov 19 2022

Keywords

• easy
• nonn

Comments

M has 2 parents, 4 grandparents, and so on up to 2^n ancestors at the top of the tree.

The genetic relatives of M are all descendants of the ancestors.

M is a genetic relative of himself or herself.

Links

• Paolo Xausa, Table of n, a(n) for n = 0..1000
• Hans Braxmeier, Calculating the number of genetic relative people in a genealogical tree.
• Index entries for linear recurrences with constant coefficients, signature (11,-26,16).

Crossrefs

Cf. A000079, A108019.

Other numbers of children: A076024 (2), A358504 (3), A358599 (5), A358600 (6), A358601 (7).

Programs

Mathematica

A358598[n_] := 2^n + 4*(8^n-1)/7; Array[A358598, 25, 0] (* or *)
LinearRecurrence[{11, -26, 16}, {1, 6, 40}, 25] (* Paolo Xausa, Feb 09 2024 *)

Python

for n in range(0,10): print(2**n+4*(8**n-1)//7)

Formula

a(n) = 2^n + 4*(8^n - 1)/7.

a(n) = A000079(n) + A108019(n). - Michel Marcus, Nov 25 2022

From Stefano Spezia, Nov 25 2022: (Start)

O.g.f.: (1 - 5*x)/((1 - x)*(1 - 2*x)*(1 - 8*x)).

E.g.f.: exp(x)*(4*(exp(7*x) - 1) + 7*exp(x))/7.

a(n) = 11*a(n-1) - 26*a(n-2) + 16*a(n-3) for n > 2. (End)