cp's OEIS Frontend

A358599 Number of genetic relatives of a person M in a genealogical tree extending back n generations and where everyone has 5 children down to the generation of M.

%I A358599 #26 Jun 19 2025 21:07:45
%S A358599 1,7,59,563,5571,55587,555619,5555683,55555811,555556067,5555556579,
%T A358599 55555557603,555555559651,5555555563747,55555555571939,
%U A358599 555555555588323,5555555555621091,55555555555686627,555555555555817699,5555555555556079843,55555555555556604131
%N A358599 Number of genetic relatives of a person M in a genealogical tree extending back n generations and where everyone has 5 children down to the generation of M.
%C A358599 M has 2 parents, 4 grandparents, and so on up to 2^n top ancestors at the top of the tree.
%C A358599 The genetic relatives of M are all descendants of those ancestors.
%C A358599 M is a genetic relative of himself or herself.
%H A358599 Hans Braxmeier, <a href="https://braxmeier.com/pages/numberOfRelatives.html">Calculating the number of genetic relative people in a genealogical tree</a>.
%H A358599 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (13,-32,20).
%F A358599 a(n) = 2^n + 5*(10^n - 1)/9.
%F A358599 a(n) = A000079(n) + A002279(n).
%F A358599 G.f.: (6*x-1)/((x-1)*(2*x-1)*(10*x-1)). - _Alois P. Heinz_, Dec 05 2022
%F A358599 a(n) = 13*a(n-1) - 32*a(n-2) + 20*a(n-3). - _Wesley Ivan Hurt_, Jun 19 2025
%t A358599 LinearRecurrence[{13, -32, 20}, {1, 7, 59}, 21] (* _Hugo Pfoertner_, Dec 05 2022 *)
%o A358599 (Python) print([2**n+5*(10**n-1)//9 for n in range(10)])
%Y A358599 Other numbers of children: A076024 (2), A358504 (3), A358598 (4), A358600 (6), A358601 (7).
%Y A358599 Cf. A000079, A002279.
%K A358599 nonn,easy
%O A358599 0,2
%A A358599 _Hans Braxmeier_, Nov 23 2022