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 1-3 of 3 results.

A133887 Binomial(n+7,n) mod 7^2.

Original entry on oeis.org

1, 8, 36, 22, 36, 8, 1, 2, 16, 23, 44, 23, 16, 2, 3, 24, 10, 17, 10, 24, 3, 4, 32, 46, 39, 46, 32, 4, 5, 40, 33, 12, 33, 40, 5, 6, 48, 20, 34, 20, 48, 6, 7, 7, 7, 7, 7, 7, 7, 8, 15, 43, 29, 43, 15, 8, 9, 23, 30, 2, 30, 23, 9, 10, 31, 17, 24, 17, 31, 10, 11, 39, 4, 46, 4, 39, 11, 12, 47
Offset: 0

Views

Author

Hieronymus Fischer, Oct 10 2007

Keywords

Comments

Periodic with length 7^3=343.

Links

Crossrefs

Cf. A000040, A133620-A133625, A133630, A038509, A133634-A133636.
Cf. A133877, A133880, A133890, A133900, A133910.
For the sequence regarding binomial(n+7, n) mod 7 see A133877.

Programs

  • Mathematica
    Table[Mod[Binomial[n+7,n],49],{n,0,80}] (* Harvey P. Dale, Apr 08 2018 *)

Formula

a(n)=binomial(n+7,7) mod 7^2.
G.f. g(x)=sum{0<=k<343, a(k)*x^k}/(1-x^343).

A133891 a(n) = binomial(n+p,n) mod p, where p=12.

Original entry on oeis.org

1, 1, 7, 11, 8, 8, 0, 0, 6, 2, 2, 2, 4, 4, 4, 0, 3, 3, 9, 9, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 8, 8, 5, 9, 3, 3, 8, 8, 8, 4, 10, 10, 6, 6, 0, 0, 0, 0, 3, 3, 9, 9, 0, 0, 4, 4, 4, 8, 8, 8, 0, 0, 0, 8, 5, 5, 7, 7, 4, 0, 0, 0, 6, 6, 6, 6, 0, 0, 0, 0, 3, 7, 1, 1, 8, 8, 8, 0, 0, 0, 8, 8, 8, 4, 4, 4, 9, 9, 3, 3, 0, 0, 0, 0
Offset: 0

Views

Author

Hieronymus Fischer, Oct 16 2007

Keywords

Comments

Periodic with length 6*12^2 = 864 = A133900(12).

Crossrefs

Cf. A000040, A133620-A133625, A133630, A038509, A133634-A133636, A133910.
See A133872, A133873, A133875, A133877, A133884, A133886, A133888, A133889, A133890 for sequences with different values of p.
See A133900 for the respective periods regarding other values of p.

Programs

  • Mathematica
    Table[Mod[Binomial[n+12,n],12],{n,0,110}] (* Harvey P. Dale, Oct 13 2017 *)

Formula

a(n) = binomial(n+12,12) mod 12.

A133897 Numbers m such that binomial(m+7,m) mod 7 = 0.

Original entry on oeis.org

42, 43, 44, 45, 46, 47, 48, 91, 92, 93, 94, 95, 96, 97, 140, 141, 142, 143, 144, 145, 146, 189, 190, 191, 192, 193, 194, 195, 238, 239, 240, 241, 242, 243, 244, 287, 288, 289, 290, 291, 292, 293, 336, 337, 338, 339, 340, 341, 342, 385, 386, 387, 388, 389, 390
Offset: 0

Views

Author

Hieronymus Fischer, Oct 20 2007

Keywords

Comments

Also numbers m such that floor(1+(m/7)) mod 7 = 0.
Partial sums of the sequence 42,1,1,1,1,1,1,43,1,1,1,1,1,1,43,... which has period 7.

Links

Crossrefs

Cf. A000040, A133620, A133621, A133623, A133630, A133635.
Cf. A133877, A133887, A133890, A133900, A133910.

Programs

  • Mathematica
    Select[Range[390],Mod[Binomial[#+7,#],7]==0&] (* or *) LinearRecurrence[{1,0,0,0,0,0,1,-1},{42, 43, 44, 45, 46, 47, 48, 91},55] (* James C. McMahon, Mar 30 2025 *)

Formula

a(n) = 7*n + 42 - 6*(n mod 7).
G.f.: (42+x+x^2+x^3+x^4+x^5+x^6+x^7)/((1-x^7)(1-x)).
G.f.: (42-41x-x^8) /((1-x^7)(1-x)^2).
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.