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A358601 Number of genetic relatives of a person M in a genealogical tree extending back n generations and where everyone has 7 children down to the generation of M. 5
1, 9, 109, 1485, 20701, 289629, 4054429, 56761245, 794655901, 11125179549, 155752507549, 2180535093405, 30527491283101, 427384877914269, 5983388290701469, 83767436069623965, 1172744104974342301, 16418417469640005789, 229857844574958508189 (list; graph; refs; listen; history; text; internal format)
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.
LINKS
FORMULA
a(n) = 2^n + 7*(14^n - 1)/13.
G.f.: (8*x-1)/((x-1)*(2*x-1)*(14*x-1)). - Alois P. Heinz, Dec 04 2022
MATHEMATICA
A358601[n_] := 2^n + 7*(14^n-1)/13; Array[A358601, 25, 0] (* or *)
LinearRecurrence[{17, -44, 28}, {1, 9, 109}, 25] (* Paolo Xausa, Feb 09 2024 *)
PROG
(Python) print([2**n+7*(14**n-1)//13 for n in range(10)])
CROSSREFS
Other numbers of children: A076024 (2), A358504 (3), A358598 (4), A358599 (5), A358600 (6).
Sequence in context: A128876 A199030 A288692 * A349335 A291815 A261502
KEYWORD
nonn,easy
AUTHOR
Hans Braxmeier, Nov 23 2022
STATUS
approved

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Last modified July 23 17:49 EDT 2024. Contains 374553 sequences. (Running on oeis4.)