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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.
4
1, 7, 59, 563, 5571, 55587, 555619, 5555683, 55555811, 555556067, 5555556579, 55555557603, 555555559651, 5555555563747, 55555555571939, 555555555588323, 5555555555621091, 55555555555686627, 555555555555817699, 5555555555556079843, 55555555555556604131
OFFSET
0,2
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.
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
MATHEMATICA
LinearRecurrence[{13, -32, 20}, {1, 7, 59}, 21] (* Hugo Pfoertner, Dec 05 2022 *)
PROG
(Python) print([2**n+5*(10**n-1)//9 for n in range(10)])
CROSSREFS
Other numbers of children: A076024 (2), A358504 (3), A358598 (4), A358600 (6), A358601 (7).
Sequence in context: A101487 A210397 A099659 * A135150 A077409 A192458
KEYWORD
nonn,easy
AUTHOR
Hans Braxmeier, Nov 23 2022
STATUS
approved