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A358599
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Number of genetic relatives of a person M in a genealogical tree extending back n generations and where everyone has 5 children down to the generation of M.
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4
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1, 7, 59, 563, 5571, 55587, 555619, 5555683, 55555811, 555556067, 5555556579, 55555557603, 555555559651, 5555555563747, 55555555571939, 555555555588323, 5555555555621091, 55555555555686627, 555555555555817699, 5555555555556079843, 55555555555556604131
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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..20.
Hans Braxmeier, Calculating the number of genetic relative people in a genealogical tree.
Index entries for linear recurrences with constant coefficients, signature (13,-32,20).
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FORMULA
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a(n) = 2^n + 5*(10^n - 1)/9.
a(n) = A000079(n) + A002279(n).
G.f.: (6*x-1)/((x-1)*(2*x-1)*(10*x-1)). - Alois P. Heinz, Dec 05 2022
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MATHEMATICA
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LinearRecurrence[{13, -32, 20}, {1, 7, 59}, 21] (* Hugo Pfoertner, Dec 05 2022 *)
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PROG
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(Python) print([2**n+5*(10**n-1)//9 for n in range(10)])
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CROSSREFS
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Other numbers of children: A076024 (2), A358504 (3), A358598 (4), A358600 (6), A358601 (7).
Cf. A000079, A002279.
Sequence in context: A101487 A210397 A099659 * A135150 A077409 A192458
Adjacent sequences: A358591 A358592 A358598 * A358600 A358601 A358602
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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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