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A358598
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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.
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4
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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
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0,2
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=0..21.
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).
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FORMULA
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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)
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PROG
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(Python) for n in range(0, 10): print(2**n+4*(8**n-1)//7)
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CROSSREFS
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Cf. A000079, A108019.
Other numbers of children: A076024 (2), A358504 (3), A358599 (5), A358600 (6), A358601 (7).
Sequence in context: A081337 A316912 A138240 * A083805 A181571 A231126
Adjacent sequences: A358590 A358591 A358592 * A358599 A358600 A358601
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KEYWORD
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easy,nonn
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AUTHOR
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Hans Braxmeier, Nov 19 2022
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STATUS
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approved
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