A358600 Number of genetic relatives of a person M in a genealogical tree extending back n generations and where everyone has 6 children down to the generation of M.

1, 8, 82, 950, 11326, 135758, 1628782, 19544750, 234535726, 2814426158, 33773108782, 405277295150, 4863327521326, 58359930214958, 700319162497582, 8403829949807150, 100845959397358126, 1210151512767642158, 14521818153210395182, 174261817838522120750

Offset: 0

Author

Hans Braxmeier, Nov 23 2022

Keywords

• nonn
• easy

Comments

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

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

M is a genetic relative of himself or herself.

Links

• Hans Braxmeier, Calculating the number of genetic relative people in a genealogical tree.
• Index entries for linear recurrences with constant coefficients, signature (15,-38,24).

Crossrefs

Other numbers of children: A076024 (2), A358504 (3), A358598 (4), A358599 (5), A358601 (7).

Programs

Mathematica

LinearRecurrence[{15, -38, 24}, {1, 8, 82}, 20] (* Hugo Pfoertner, Dec 05 2022 *)

Python

print([2**n+6*(12**n-1)//11 for n in range(10)])

Formula

a(n) = 2^n + 6*(12^n - 1)/11.

G.f.: (1 - 7*x)/((1 - x)*(1 - 2*x)*(1 - 12*x)). - Stefano Spezia, Dec 05 2022