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%I #29 Feb 09 2024 08:41:01
%S 1,9,109,1485,20701,289629,4054429,56761245,794655901,11125179549,
%T 155752507549,2180535093405,30527491283101,427384877914269,
%U 5983388290701469,83767436069623965,1172744104974342301,16418417469640005789,229857844574958508189
%N 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.
%C M has 2 parents, 4 grandparents, and so on up to 2^n top ancestors at the top of the tree.
%C The genetic relatives of M are all descendants of those ancestors.
%C M is a genetic relative of himself or herself.
%H Paolo Xausa, <a href="/A358601/b358601.txt">Table of n, a(n) for n = 0..750</a>
%H Hans Braxmeier, <a href="https://braxmeier.com/pages/numberOfRelatives/numberOfRelatives.html">Calculating the number of genetic relative people in a genealogical tree</a>.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (17,-44,28).
%F a(n) = 2^n + 7*(14^n - 1)/13.
%F G.f.: (8*x-1)/((x-1)*(2*x-1)*(14*x-1)). - _Alois P. Heinz_, Dec 04 2022
%t A358601[n_] := 2^n + 7*(14^n-1)/13; Array[A358601, 25, 0] (* or *)
%t LinearRecurrence[{17, -44, 28}, {1, 9, 109}, 25] (* _Paolo Xausa_, Feb 09 2024 *)
%o (Python) print([2**n+7*(14**n-1)//13 for n in range(10)])
%Y Other numbers of children: A076024 (2), A358504 (3), A358598 (4), A358599 (5), A358600 (6).
%K nonn,easy
%O 0,2
%A _Hans Braxmeier_, Nov 23 2022
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