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A358598 Number of genetic relatives of a person M in a genealogical tree extending back n generations and where everyone has 4 children down to the generation of M.

%I A358598 #33 Feb 09 2024 07:44:59
%S A358598 1,6,40,300,2356,18756,149860,1198500,9587236,76696356,613567780,
%T A358598 4908536100,39268276516,314146187556,2513169451300,20105355512100,
%U A358598 160842843900196,1286742750808356,10293942005680420,82351536043870500,658812288347818276,5270498306776254756
%N A358598 Number of genetic relatives of a person M in a genealogical tree extending back n generations and where everyone has 4 children down to the generation of M.
%C A358598 M has 2 parents, 4 grandparents, and so on up to 2^n ancestors at the top of the tree.
%C A358598 The genetic relatives of M are all descendants of the ancestors.
%C A358598 M is a genetic relative of himself or herself.
%H A358598 Paolo Xausa, <a href="/A358598/b358598.txt">Table of n, a(n) for n = 0..1000</a>
%H A358598 Hans Braxmeier, <a href="https://braxmeier.com/pages/numberOfRelatives/numberOfRelatives.html">Calculating the number of genetic relative people in a genealogical tree</a>.
%H A358598 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (11,-26,16).
%F A358598 a(n) = 2^n + 4*(8^n - 1)/7.
%F A358598 a(n) = A000079(n) + A108019(n). - _Michel Marcus_, Nov 25 2022
%F A358598 From _Stefano Spezia_, Nov 25 2022: (Start)
%F A358598 O.g.f.: (1 - 5*x)/((1 - x)*(1 - 2*x)*(1 - 8*x)).
%F A358598 E.g.f.: exp(x)*(4*(exp(7*x) - 1) + 7*exp(x))/7.
%F A358598 a(n) = 11*a(n-1) - 26*a(n-2) + 16*a(n-3) for n > 2. (End)
%t A358598 A358598[n_] := 2^n + 4*(8^n-1)/7; Array[A358598, 25, 0] (* or *)
%t A358598 LinearRecurrence[{11, -26, 16}, {1, 6, 40}, 25] (* _Paolo Xausa_, Feb 09 2024 *)
%o A358598 (Python) for n in range(0,10): print(2**n+4*(8**n-1)//7)
%Y A358598 Cf. A000079, A108019.
%Y A358598 Other numbers of children: A076024 (2), A358504 (3), A358599 (5), A358600 (6), A358601 (7).
%K A358598 easy,nonn
%O A358598 0,2
%A A358598 _Hans Braxmeier_, Nov 19 2022