cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

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

Views

Author

Hans Braxmeier, Nov 19 2022

Keywords

Comments

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.

Links

Crossrefs

Cf. A000079, A108019.
Other numbers of children: A076024 (2), A358504 (3), A358599 (5), A358600 (6), A358601 (7).

Programs

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

Formula

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)

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

Views

Author

Hans Braxmeier, Nov 23 2022

Keywords

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

Crossrefs

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

Programs

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

Formula

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

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.

Original entry on oeis.org

1, 7, 59, 563, 5571, 55587, 555619, 5555683, 55555811, 555556067, 5555556579, 55555557603, 555555559651, 5555555563747, 55555555571939, 555555555588323, 5555555555621091, 55555555555686627, 555555555555817699, 5555555555556079843, 55555555555556604131
Offset: 0

Views

Author

Hans Braxmeier, Nov 23 2022

Keywords

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

Crossrefs

Other numbers of children: A076024 (2), A358504 (3), A358598 (4), A358600 (6), A358601 (7).
Cf. A000079, A002279.

Programs

  • Mathematica
    LinearRecurrence[{13, -32, 20}, {1, 7, 59}, 21] (* Hugo Pfoertner, Dec 05 2022 *)
  • Python
    print([2**n+5*(10**n-1)//9 for n in range(10)])

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
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

Views

Author

Hans Braxmeier, Nov 23 2022

Keywords

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

Crossrefs

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

Programs

  • Mathematica
    LinearRecurrence[{15, -38, 24}, {1, 8, 82}, 20] (* Hugo Pfoertner, Dec 05 2022 *)
  • Python
    print([2**n+6*(12**n-1)//11 for n in range(10)])

Formula

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
Showing 1-4 of 4 results.

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