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.

1, 7, 59, 563, 5571, 55587, 555619, 5555683, 55555811, 555556067, 5555556579, 55555557603, 555555559651, 5555555563747, 55555555571939, 555555555588323, 5555555555621091, 55555555555686627, 555555555555817699, 5555555555556079843, 55555555555556604131

Offset: 0

Author

Hans Braxmeier, Nov 23 2022

Keywords

• nonn
• easy

Comments

M has 2 parents, 4 grandparents, and so on up to 2^n top ancestors at the top of the tree.

The genetic relatives of M are all descendants of those ancestors.

M is a genetic relative of himself or herself.

Links

• Hans Braxmeier, Calculating the number of genetic relative people in a genealogical tree.
• Index entries for linear recurrences with constant coefficients, signature (13,-32,20).

Crossrefs

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

Cf. A000079, A002279.

Programs

Mathematica

LinearRecurrence[{13, -32, 20}, {1, 7, 59}, 21] (* Hugo Pfoertner, Dec 05 2022 *)

Python

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

Formula

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

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

G.f.: (6*x-1)/((x-1)*(2*x-1)*(10*x-1)). - Alois P. Heinz, Dec 05 2022

a(n) = 13*a(n-1) - 32*a(n-2) + 20*a(n-3). - Wesley Ivan Hurt, Jun 19 2025