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.

A047307 Numbers that are congruent to {3, 4, 5, 6} mod 7.

Original entry on oeis.org

3, 4, 5, 6, 10, 11, 12, 13, 17, 18, 19, 20, 24, 25, 26, 27, 31, 32, 33, 34, 38, 39, 40, 41, 45, 46, 47, 48, 52, 53, 54, 55, 59, 60, 61, 62, 66, 67, 68, 69, 73, 74, 75, 76, 80, 81, 82, 83, 87, 88, 89, 90, 94, 95, 96, 97, 101, 102, 103, 104, 108, 109, 110, 111
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A047288, A047389.

Programs

  • Magma
    [n : n in [0..150] | n mod 7 in [3, 4, 5, 6]]; // Wesley Ivan Hurt, Jun 02 2016
  • Maple
    A047307:=n->(14*n+1-3*I^(2*n)-(3-3*I)*I^(-n)-(3+3*I)*I^n)/8: seq(A047307(n), n=1..100); # Wesley Ivan Hurt, Jun 02 2016
  • Mathematica
    Table[(14n+1-3*I^(2*n)-(3-3*I)*I^(-n)-(3+3*I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, Jun 02 2016 *)
LinearRecurrence[{1,0,0,1,-1},{3,4,5,6,10},70] (* Harvey P. Dale, Dec 28 2024 *)

Formula

G.f.: x*(3+x+x^2+x^3+x^4) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 25 2011
From Wesley Ivan Hurt, Jun 02 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(n) = (14*n+1-3*i^(2*n)-(3-3*i)*i^(-n)-(3+3*i)*i^n)/8 where i=sqrt(-1).
a(2k) = A047288(k), a(2k-1) = A047389(k). (End)

A047312 Numbers that are congruent to {0, 4, 5, 6} mod 7.

Original entry on oeis.org

0, 4, 5, 6, 7, 11, 12, 13, 14, 18, 19, 20, 21, 25, 26, 27, 28, 32, 33, 34, 35, 39, 40, 41, 42, 46, 47, 48, 49, 53, 54, 55, 56, 60, 61, 62, 63, 67, 68, 69, 70, 74, 75, 76, 77, 81, 82, 83, 84, 88, 89, 90, 91, 95, 96, 97, 98, 102, 103, 104, 105, 109, 110, 111
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A047288, A047382.

Programs

  • Magma
    [n : n in [0..150] | n mod 7 in [0, 4, 5, 6]]; // Wesley Ivan Hurt, Jun 03 2016
  • Maple
    A047312:=n->(14*n-5+3*I^(2*n)-(3+3*I)*I^(-n)-(3-3*I)*I^n)/8: seq(A047312(n), n=1..100); # Wesley Ivan Hurt, Jun 03 2016
  • Mathematica
    Table[(14n-5+3*I^(2n)-(3+3*I)*I^(-n)-(3-3*I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, Jun 03 2016 *)

Formula

G.f.: x^2*(4+x+x^2+x^3) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 25 2011
From Wesley Ivan Hurt, Jun 03 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(n) = (14*n-5+3*i^(2*n)-(3+3*i)*i^(-n)-(3-3*i)*i^n)/8 where i=sqrt(-1).
a(2k) = A047288(k), a(2k-1) = A047382(k). (End)

A047313 Numbers that are congruent to {1, 4, 5, 6} mod 7.

Original entry on oeis.org

1, 4, 5, 6, 8, 11, 12, 13, 15, 18, 19, 20, 22, 25, 26, 27, 29, 32, 33, 34, 36, 39, 40, 41, 43, 46, 47, 48, 50, 53, 54, 55, 57, 60, 61, 62, 64, 67, 68, 69, 71, 74, 75, 76, 78, 81, 82, 83, 85, 88, 89, 90, 92, 95, 96, 97, 99, 102, 103, 104, 106, 109, 110, 111
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A047288, A047383.

Programs

Formula

G.f.: x*(1+3*x+x^2+x^3+x^4) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Dec 03 2011
From Wesley Ivan Hurt, May 23 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(n) = (14n-3+i^(2n)-(3+i)*i^(-n)-(3-i)*i^n)/8 where i=sqrt(-1).
a(2n) = A047288(n), a(2n-1) = A047383(n). (End)
E.g.f.: (4 - sin(x) - 3*cos(x) + (7*x - 2)*sinh(x) + (7*x - 1)*cosh(x))/4. - Ilya Gutkovskiy, May 24 2016

A047315 Numbers that are congruent to {2, 4, 5, 6} mod 7.

Original entry on oeis.org

2, 4, 5, 6, 9, 11, 12, 13, 16, 18, 19, 20, 23, 25, 26, 27, 30, 32, 33, 34, 37, 39, 40, 41, 44, 46, 47, 48, 51, 53, 54, 55, 58, 60, 61, 62, 65, 67, 68, 69, 72, 74, 75, 76, 79, 81, 82, 83, 86, 88, 89, 90, 93, 95, 96, 97, 100, 102, 103, 104, 107, 109, 110, 111
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A047288, A047385.

Programs

  • Magma
    [n : n in [0..150] | n mod 7 in [2, 4, 5, 6]]; // Wesley Ivan Hurt, Jun 03 2016
  • Maple
    A047315:=n->(14*n-1-I^(2*n)-(3-I)*I^(-n)-(3+I)*I^n)/8: seq(A047315(n), n=1..100); # Wesley Ivan Hurt, Jun 03 2016
  • Mathematica
    Table[(14n-1-I^(2n)-(3-I)*I^(-n)-(3+I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, Jun 03 2016 *)
Select[Range[200],MemberQ[{2,4,5,6},Mod[#,7]]&] (* or *) LinearRecurrence[ {1,0,0,1,-1},{2,4,5,6,9},100] (* Harvey P. Dale, Jan 19 2019 *)

Formula

G.f.: x*(2+2*x+x^2+x^3+x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 03 2011
From Wesley Ivan Hurt, Jun 03 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(n) = (14*n-1-i^(2*n)-(3-i)*i^(-n)-(3+i)*i^n)/8 where i=sqrt(-1).
a(2k) = A047288(k), a(2k-1) = A047385(k). (End)
Showing 1-4 of 4 results.

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

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