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, 3218009824049415968925

Offset

0,2

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).

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

E.g.f.: exp(2*x) + (7/13)*exp(x)*(exp(13*x) - 1). - Stefano Spezia, Feb 03 2026

a(n) = 17*a(n-1) - 44*a(n-2) + 28*a(n-3). - Wesley Ivan Hurt, Feb 13 2026

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 *)

Prog

(Python) print([2**n+7*(14**n-1)//13 for n in range(10)])
(Magma) [2^n + 7*(14^n - 1)/13 : n in [0..20]]; // Wesley Ivan Hurt, Feb 13 2026

Crossrefs

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

Sequence in context: A199030 A391542 A288692 * A388913 A349335 A291815

Adjacent sequences: A358598 A358599 A358600 * A358602 A358603 A358604

Keyword

nonn,easy

Author

Hans Braxmeier, Nov 23 2022

Status

approved