A358599 - OEIS

%I #24 Dec 06 2022 15:48:25

%S 1,7,59,563,5571,55587,555619,5555683,55555811,555556067,5555556579,

%T 55555557603,555555559651,5555555563747,55555555571939,

%U 555555555588323,5555555555621091,55555555555686627,555555555555817699,5555555555556079843,55555555555556604131

%N 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 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 (13,-32,20).

%F a(n) = 2^n + 5*(10^n - 1)/9.

%F a(n) = A000079(n) + A002279(n).

%F G.f.: (6*x-1)/((x-1)*(2*x-1)*(10*x-1)). - _Alois P. Heinz_, Dec 05 2022

%t LinearRecurrence[{13, -32, 20}, {1, 7, 59}, 21] (* _Hugo Pfoertner_, Dec 05 2022 *)

%o (Python) print([2**n+5*(10**n-1)//9 for n in range(10)])

%Y Other numbers of children: A076024 (2), A358504 (3), A358598 (4), A358600 (6), A358601 (7).

%Y Cf. A000079, A002279.

%K nonn,easy

%O 0,2

%A _Hans Braxmeier_, Nov 23 2022