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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 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 (11,-26,16). 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 Cf. A000079, A108019. Other numbers of children: A076024 (2), A358504 (3), A358599 (5), A358600 (6), A358601 (7). Sequence in context: A366199 A373622 A138240 * A083805 A181571 A231126 Adjacent sequences: A358595 A358596 A358597 * A358599 A358600 A358601 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.)