

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
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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.
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(n1)  26*a(n2) + 16*a(n3) for n > 2. (End)


MATHEMATICA

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**n1)//7)


CROSSREFS



KEYWORD

easy,nonn


AUTHOR



STATUS

approved



