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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. 5
1, 6, 40, 300, 2356, 18756, 149860, 1198500, 9587236, 76696356, 613567780, 4908536100, 39268276516, 314146187556, 2513169451300, 20105355512100, 160842843900196, 1286742750808356, 10293942005680420, 82351536043870500, 658812288347818276, 5270498306776254756 (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 ancestors at the top of the tree.
The genetic relatives of M are all descendants of the ancestors.
M is a genetic relative of himself or herself.
LINKS
FORMULA
a(n) = 2^n + 4*(8^n - 1)/7.
a(n) = A000079(n) + A108019(n). - Michel Marcus, Nov 25 2022
From Stefano Spezia, Nov 25 2022: (Start)
O.g.f.: (1 - 5*x)/((1 - x)*(1 - 2*x)*(1 - 8*x)).
E.g.f.: exp(x)*(4*(exp(7*x) - 1) + 7*exp(x))/7.
a(n) = 11*a(n-1) - 26*a(n-2) + 16*a(n-3) for n > 2. (End)
MATHEMATICA
A358598[n_] := 2^n + 4*(8^n-1)/7; Array[A358598, 25, 0] (* or *)
LinearRecurrence[{11, -26, 16}, {1, 6, 40}, 25] (* Paolo Xausa, Feb 09 2024 *)
PROG
(Python) for n in range(0, 10): print(2**n+4*(8**n-1)//7)
CROSSREFS
Other numbers of children: A076024 (2), A358504 (3), A358599 (5), A358600 (6), A358601 (7).
Sequence in context: A366199 A373622 A138240 * A083805 A181571 A231126
KEYWORD
easy,nonn
AUTHOR
Hans Braxmeier, Nov 19 2022
STATUS
approved

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Last modified June 13 10:24 EDT 2024. Contains 373383 sequences. (Running on oeis4.)