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A358601
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Number of genetic relatives of a person M in a genealogical tree extending back n generations and where everyone has 7 children down to the generation of M.
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4
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1, 9, 109, 1485, 20701, 289629, 4054429, 56761245, 794655901, 11125179549, 155752507549, 2180535093405, 30527491283101, 427384877914269, 5983388290701469, 83767436069623965, 1172744104974342301, 16418417469640005789, 229857844574958508189
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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 top 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.
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LINKS
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Table of n, a(n) for n=0..18.
Hans Braxmeier, Calculating the number of genetic relative people in a genealogical tree.
Index entries for linear recurrences with constant coefficients, signature (17,-44,28).
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FORMULA
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a(n) = 2^n + 7*(14^n - 1)/13.
G.f.: (8*x-1)/((x-1)*(2*x-1)*(14*x-1)). - Alois P. Heinz, Dec 04 2022
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PROG
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(Python) print([2**n+7*(14**n-1)//13 for n in range(10)])
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CROSSREFS
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Other numbers of children: A076024 (2), A358504 (3), A358598 (4), A358599 (5), A358600 (6).
Sequence in context: A128876 A199030 A288692 * A349335 A291815 A261502
Adjacent sequences: A358598 A358599 A358600 * A358602 A358603 A358604
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KEYWORD
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nonn,easy
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AUTHOR
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Hans Braxmeier, Nov 23 2022
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STATUS
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approved
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