

A358504


Number of genetic relatives of a person M in a genealogical tree extending back n generations and where everyone has 3 children down to the generation of M.


5



1, 5, 25, 137, 793, 4697, 28057, 168089, 1008025, 6047129, 36280729, 217680281, 1306073497, 7836424601, 47018514841, 282111023513, 1692666010009, 10155995797913, 60935974263193, 365615844530585, 2193695065086361, 13162170386323865, 78973022309554585
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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 those ancestors.
M is a genetic relative of himself or herself.


LINKS



FORMULA

a(n) = 2^n + 3*(6^n  1)/5.


EXAMPLE

For n=2, the tree comprises a(2) = 25 people,
GG GG G = 4 grandparents
/  \ /  \ P = 2 parents
U U PP U U S = 2 siblings
/\ /\ /\ /\ /\ U = 4 uncles (or aunts)
C C C C C C S M S C C C C C C C = 12 cousins
The spouses of U are not shown and are not genetic relatives of M.


MATHEMATICA

LinearRecurrence[{9, 20, 12}, {1, 5, 25}, 25] (* Paolo Xausa, Feb 09 2024 *)


PROG

(Python) for n in range(0, 23): print(2**n+3*(6**n1)//5)
(PARI) a(n) = (3^(n+1)+5)<<n \ 5; \\ Kevin Ryde, Nov 23 2022


CROSSREFS



KEYWORD

easy,nonn


AUTHOR



STATUS

approved



