Hans Braxmeier - cp's OEIS frontend

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.

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

Offset: 0

Hans Braxmeier, Nov 23 2022

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.

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).

Other numbers of children: A076024 (2), A358504 (3), A358598 (4), A358600 (6), A358601 (7).

Cf. A000079, A002279.

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

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

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
a(n) = 13*a(n-1) - 32*a(n-2) + 20*a(n-3). - Wesley Ivan Hurt, Jun 19 2025

A358600 Number of genetic relatives of a person M in a genealogical tree extending back n generations and where everyone has 6 children down to the generation of M.

Original entry on oeis.org

1, 8, 82, 950, 11326, 135758, 1628782, 19544750, 234535726, 2814426158, 33773108782, 405277295150, 4863327521326, 58359930214958, 700319162497582, 8403829949807150, 100845959397358126, 1210151512767642158, 14521818153210395182, 174261817838522120750

Offset: 0

Hans Braxmeier, Nov 23 2022

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.

Hans Braxmeier, Calculating the number of genetic relative people in a genealogical tree.
Index entries for linear recurrences with constant coefficients, signature (15,-38,24).

Other numbers of children: A076024 (2), A358504 (3), A358598 (4), A358599 (5), A358601 (7).

LinearRecurrence[{15, -38, 24}, {1, 8, 82}, 20] (* Hugo Pfoertner, Dec 05 2022 *)

print([2**n+6*(12**n-1)//11 for n in range(10)])

a(n) = 2^n + 6*(12^n - 1)/11.

G.f.: (1 - 7*x)/((1 - x)*(1 - 2*x)*(1 - 12*x)). - Stefano Spezia, Dec 05 2022

A358601 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.

Original entry on oeis.org

1, 9, 109, 1485, 20701, 289629, 4054429, 56761245, 794655901, 11125179549, 155752507549, 2180535093405, 30527491283101, 427384877914269, 5983388290701469, 83767436069623965, 1172744104974342301, 16418417469640005789, 229857844574958508189

Offset: 0

Hans Braxmeier, Nov 23 2022

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.

Paolo Xausa, Table of n, a(n) for n = 0..750
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).

Other numbers of children: A076024 (2), A358504 (3), A358598 (4), A358599 (5), A358600 (6).

A358601[n_] := 2^n + 7*(14^n-1)/13; Array[A358601, 25, 0] (* or *)
LinearRecurrence[{17, -44, 28}, {1, 9, 109}, 25] (* Paolo Xausa, Feb 09 2024 *)

print([2**n+7*(14**n-1)//13 for n in range(10)])

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

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.

Original entry on oeis.org

1, 6, 40, 300, 2356, 18756, 149860, 1198500, 9587236, 76696356, 613567780, 4908536100, 39268276516, 314146187556, 2513169451300, 20105355512100, 160842843900196, 1286742750808356, 10293942005680420, 82351536043870500, 658812288347818276, 5270498306776254756

Offset: 0

Hans Braxmeier, Nov 19 2022

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.

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).

Cf. A000079, A108019.

Other numbers of children: A076024 (2), A358504 (3), A358599 (5), A358600 (6), A358601 (7).

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 *)

for n in range(0,10): print(2**n+4*(8**n-1)//7)

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)

A358504 Number of genetic relatives of a person M in a genealogical tree extending back n generations and where everyone has 3 children down to the generation of M.

Original entry on oeis.org

1, 5, 25, 137, 793, 4697, 28057, 168089, 1008025, 6047129, 36280729, 217680281, 1306073497, 7836424601, 47018514841, 282111023513, 1692666010009, 10155995797913, 60935974263193, 365615844530585, 2193695065086361, 13162170386323865, 78973022309554585

Offset: 0

Hans Braxmeier, Nov 19 2022

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 those ancestors.
M is a genetic relative of himself or herself.

			For n=2, the tree comprises a(2) = 25 people,
      G-------G       G-------G       G = 4 grandparents
     /    |    \     /    |    \      P = 2 parents
    U     U     P---P     U     U     S = 2 siblings
   /|\   /|\     /|\     /|\   /|\    U = 4 uncles (or aunts)
  C C C C C C   S M S   C C C C C C   C = 12 cousins
The spouses of U are not shown and are not genetic relatives of M.

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 (9,-20,12).

Cf. A154407.

Other numbers of children: A076024 (2), A358598 (4), A358599 (5), A358600 (6), A358601 (7).

A358504[n_] := 2^n + 3*(6^n-1)/5; Array[A358504, 25, 0] (* or *)
LinearRecurrence[{9, -20, 12}, {1, 5, 25}, 25] (* Paolo Xausa, Feb 09 2024 *)

a(n) = (3^(n+1)+5)<Kevin Ryde, Nov 23 2022

for n in range(0,23): print(2**n+3*(6**n-1)//5)

a(n) = 2^n + 3*(6^n - 1)/5.

a(n) = 2*(A154407(n) + 1)/5 - 1. - Hugo Pfoertner, Nov 22 2022

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User: Hans Braxmeier

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.

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A358600 Number of genetic relatives of a person M in a genealogical tree extending back n generations and where everyone has 6 children down to the generation of M.

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A358601 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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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.

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A358504 Number of genetic relatives of a person M in a genealogical tree extending back n generations and where everyone has 3 children down to the generation of M.

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