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A358600 Number of genetic relatives of a person M in a genealogical tree extending back n generations and where everyone has 6 children down to the generation of M. 4

%I #24 Dec 06 2022 03:22:45

%S 1,8,82,950,11326,135758,1628782,19544750,234535726,2814426158,

%T 33773108782,405277295150,4863327521326,58359930214958,

%U 700319162497582,8403829949807150,100845959397358126,1210151512767642158,14521818153210395182,174261817838522120750

%N Number of genetic relatives of a person M in a genealogical tree extending back n generations and where everyone has 6 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 Hans Braxmeier, <a href="https://braxmeier.com/pages/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 (15,-38,24).

%F a(n) = 2^n + 6*(12^n - 1)/11.

%F G.f.: (1 - 7*x)/((1 - x)*(1 - 2*x)*(1 - 12*x)). - _Stefano Spezia_, Dec 05 2022

%t LinearRecurrence[{15, -38, 24}, {1, 8, 82}, 20] (* _Hugo Pfoertner_, Dec 05 2022 *)

%o (Python) print([2**n+6*(12**n-1)//11 for n in range(10)])

%Y Other numbers of children: A076024 (2), A358504 (3), A358598 (4), A358599 (5), A358601 (7).

%K nonn,easy

%O 0,2

%A _Hans Braxmeier_, Nov 23 2022

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)