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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. 5
 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 Paolo Xausa, Table of n, a(n) for n = 0..1000 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. MATHEMATICA A358504[n_] := 2^n + 3*(6^n-1)/5; Array[A358504, 25, 0] (* or *) 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**n-1)//5) (PARI) a(n) = (3^(n+1)+5)<

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Last modified August 7 01:21 EDT 2024. Contains 375002 sequences. (Running on oeis4.)