cp's OEIS Frontend

A358504 Number of genetic relatives of a person M in a genealogical tree extending back n generations and where everyone has 3 children down to the generation of M.

%I A358504 #58 Mar 24 2025 04:11:10
%S A358504 1,5,25,137,793,4697,28057,168089,1008025,6047129,36280729,217680281,
%T A358504 1306073497,7836424601,47018514841,282111023513,1692666010009,
%U A358504 10155995797913,60935974263193,365615844530585,2193695065086361,13162170386323865,78973022309554585
%N A358504 Number of genetic relatives of a person M in a genealogical tree extending back n generations and where everyone has 3 children down to the generation of M.
%C A358504 M has 2 parents, 4 grandparents, and so on up to 2^n ancestors at the top of the tree.
%C A358504 The genetic relatives of M are all descendants of those ancestors.
%C A358504 M is a genetic relative of himself or herself.
%H A358504 Paolo Xausa, <a href="/A358504/b358504.txt">Table of n, a(n) for n = 0..1000</a>
%H A358504 Hans Braxmeier, <a href="https://braxmeier.com/pages/numberOfRelatives/numberOfRelatives.html">Calculating the number of genetic relative people in a genealogical tree</a>.
%H A358504 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,-20,12).
%F A358504 a(n) = 2^n + 3*(6^n - 1)/5.
%F A358504 a(n) = 2*(A154407(n) + 1)/5 - 1. - _Hugo Pfoertner_, Nov 22 2022
%e A358504 For n=2, the tree comprises a(2) = 25 people,
%e A358504       G-------G       G-------G       G = 4 grandparents
%e A358504      /    |    \     /    |    \      P = 2 parents
%e A358504     U     U     P---P     U     U     S = 2 siblings
%e A358504    /|\   /|\     /|\     /|\   /|\    U = 4 uncles (or aunts)
%e A358504   C C C C C C   S M S   C C C C C C   C = 12 cousins
%e A358504 The spouses of U are not shown and are not genetic relatives of M.
%t A358504 A358504[n_] := 2^n + 3*(6^n-1)/5; Array[A358504, 25, 0] (* or *)
%t A358504 LinearRecurrence[{9, -20, 12}, {1, 5, 25}, 25] (* _Paolo Xausa_, Feb 09 2024 *)
%o A358504 (Python) for n in range(0,23): print(2**n+3*(6**n-1)//5)
%o A358504 (PARI) a(n) = (3^(n+1)+5)<<n \ 5; \\ _Kevin Ryde_, Nov 23 2022
%Y A358504 Cf. A154407.
%Y A358504 Other numbers of children: A076024 (2), A358598 (4), A358599 (5), A358600 (6), A358601 (7).
%K A358504 easy,nonn
%O A358504 0,2
%A A358504 _Hans Braxmeier_, Nov 19 2022