A358601 Number of genetic relatives of a person M in a genealogical tree extending back n generations and where everyone has 7 children down to the generation of M.

1, 9, 109, 1485, 20701, 289629, 4054429, 56761245, 794655901, 11125179549, 155752507549, 2180535093405, 30527491283101, 427384877914269, 5983388290701469, 83767436069623965, 1172744104974342301, 16418417469640005789, 229857844574958508189

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

• Paolo Xausa, Table of n, a(n) for n = 0..750
• Hans Braxmeier, Calculating the number of genetic relative people in a genealogical tree.
• Index entries for linear recurrences with constant coefficients, signature (17,-44,28).

Crossrefs

Other numbers of children: A076024 (2), A358504 (3), A358598 (4), A358599 (5), A358600 (6).

Programs

Mathematica

A358601[n_] := 2^n + 7*(14^n-1)/13; Array[A358601, 25, 0] (* or *)
LinearRecurrence[{17, -44, 28}, {1, 9, 109}, 25] (* Paolo Xausa, Feb 09 2024 *)

Python

print([2**n+7*(14**n-1)//13 for n in range(10)])

Formula

a(n) = 2^n + 7*(14^n - 1)/13.

G.f.: (8*x-1)/((x-1)*(2*x-1)*(14*x-1)). - Alois P. Heinz, Dec 04 2022