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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. 4
1, 5, 25, 137, 793, 4697, 28057, 168089, 1008025, 6047129, 36280729, 217680281, 1306073497, 7836424601, 47018514841, 282111023513, 1692666010009, 10155995797913, 60935974263193, 365615844530585, 2193695065086361, 13162170386323865, 78973022309554585 (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 those ancestors.

M is a genetic relative of himself or herself.

LINKS

Table of n, a(n) for n=0..22.

Hans Braxmeier, Calculating the number of genetic relative people in a genealogical tree.

Index entries for linear recurrences with constant coefficients, signature (9,-20,12).

FORMULA

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

a(n) = (2*(A154407(n) + 1)/5 - 1. - Hugo Pfoertner, Nov 22 2022

EXAMPLE

For n=2, the tree comprises a(2) = 25 people,

G-------G G-------G G = 4 grandparents

/ | \ / | \ P = 2 parents

U U P---P 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.

PROG

(Python) for n in range(0, 23): print(2**n+3*(6**n-1)//5)

(PARI) a(n) = (3^(n+1)+5)<<n \ 5; \\ Kevin Ryde, Nov 23 2022

CROSSREFS

Cf. A154407.

Other numbers of children: A076024 (2), A358598 (4), A358599 (5), A358600 (6), A358601 (7).

Sequence in context: A272706 A275905 A124891 * A094094 A344249 A081683

Adjacent sequences: A358501 A358502 A358503 * A358505 A358506 A358507

KEYWORD

easy,nonn

AUTHOR

Hans Braxmeier, Nov 19 2022

STATUS

approved

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Last modified February 8 01:34 EST 2023. Contains 360133 sequences. (Running on oeis4.)