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A358599 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. 4
1, 7, 59, 563, 5571, 55587, 555619, 5555683, 55555811, 555556067, 5555556579, 55555557603, 555555559651, 5555555563747, 55555555571939, 555555555588323, 5555555555621091, 55555555555686627, 555555555555817699, 5555555555556079843, 55555555555556604131 (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 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.

LINKS

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).

FORMULA

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

MATHEMATICA

LinearRecurrence[{13, -32, 20}, {1, 7, 59}, 21] (* Hugo Pfoertner, Dec 05 2022 *)

PROG

(Python) print([2**n+5*(10**n-1)//9 for n in range(10)])

CROSSREFS

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

KEYWORD

nonn,easy

AUTHOR

Hans Braxmeier, Nov 23 2022

STATUS

approved

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Last modified February 8 02:43 EST 2023. Contains 360133 sequences. (Running on oeis4.)