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.

A131228 3*A051340 - 2*A128174.

Original entry on oeis.org

1, 3, 4, 1, 3, 7, 3, 1, 3, 10, 1, 3, 1, 3, 13, 3, 1, 3, 1, 3, 16, 1, 3, 1, 3, 1, 3, 19, 3, 1, 3, 1, 3, 1, 3, 22, 1, 3, 1, 3, 1, 3, 25, 3, 1, 3, 1, 3, 1, 3, 1, 3, 28
Offset: 0

Views

Author

Gary W. Adamson, Jun 20 2007

Keywords

Comments

Row sums = A131229.

Examples

			First few rows of the triangle are:
1;
3, 4;
1, 3, 7;
3, 1, 3, 10;
1, 3, 1, 3, 13;
...

Crossrefs

Cf. A051340, A128174, A131229, A131227.

Formula

3*A051340 - 2*A128174 as infinite lower triangular matrices.

A131227 2*A051340 - A128174.

Original entry on oeis.org

1, 2, 3, 1, 2, 5, 2, 1, 2, 7, 1, 2, 1, 2, 9, 2, 1, 2, 1, 2, 11, 1, 2, 1, 2, 1, 2, 13, 2, 1, 2, 1, 2, 1, 2, 15, 1, 2, 1, 2, 1, 2, 1, 2, 17, 2, 1, 2, 1, 2, 1, 2, 1, 2, 19
Offset: 0

Views

Author

Gary W. Adamson, Jun 20 2007

Keywords

Comments

Row sums = A047383, numbers congruent to {1,5} mod 7: (1, 5, 8, 12, 15, 19, ...)

Examples

			First few rows of the triangle:
  1;
  2, 3;
  1, 2, 5;
  2, 1, 2, 7;
  1, 2, 1, 2, 9;
  2, 1, 2, 1, 2, 11;
  1, 2, 1, 2, 1,  2, 13;
  ...

Crossrefs

Cf. A051340, A128174, A047383, A131228, A131229.

Formula

2*A051340 - A128174 as infinite lower triangular matrices.

A131231 3*A130296 - 2*A128174.

Original entry on oeis.org

1, 6, 1, 7, 3, 1, 12, 1, 3, 1, 13, 3, 1, 3, 1, 18, 1, 3, 1, 3, 1, 19, 3, 1, 3, 1, 3, 1, 24, 1, 3, 1, 3, 1, 3, 1, 25, 3, 1, 3, 1, 3, 1, 3, 1
Offset: 1

Views

Author

Gary W. Adamson, Jun 20 2007

Keywords

Comments

Left column = A047225, numbers congruent to {0,1} mod 6: (1, 6, 7, 12, 13, 18, 19, ...).
Row sums = A131229, numbers congruent to {1,7} mod 10: (1, 7, 11, 17, ...).

Examples

			First few rows of the triangle:
   1;
   6, 1;
   7, 3, 1;
  12, 1, 3, 1;
  13, 3, 1, 3, 1;
  ...

Crossrefs

Cf. A131229, A047225, A130296, A128174.

Formula

3*A130296 - 2*A128174 as infinite lower triangular matrices.

A268044 The odd numbers congruent to {3, 4} mod 5.

Original entry on oeis.org

3, 9, 13, 19, 23, 29, 33, 39, 43, 49, 53, 59, 63, 69, 73, 79, 83, 89, 93, 99, 103, 109, 113, 119, 123, 129, 133, 139, 143, 149, 153, 159, 163, 169, 173, 179, 183, 189, 193, 199, 203, 209, 213, 219, 223, 229, 233, 239, 243, 249, 253, 259, 263, 269, 273, 279, 283, 289, 293, 299
Offset: 1

Views

Author

Mikk Heidemaa, Jan 25 2016

Keywords

Comments

The odd numbers with terminal digit 3 or 9.

Links

Crossrefs

Cf. A001622, A005408, A045435, A047204, A131229.
Second bisection of A045572.

Programs

  • Magma
    [5*n-(3-(-1)^n)/2: n in [1..60]]; // Vincenzo Librandi, Jan 25 2016
  • Mathematica
    Table[5 n - (3 - (-1)^n)/2, {n, 1000}] (* or *) Select[ Range [1000], OddQ[#] && MemberQ[{3, 4}, Mod[#, 5]] &]
LinearRecurrence[{1,1,-1},{3,9,13},60] (* Harvey P. Dale, Feb 12 2023 *)

Formula

G.f.: x*(3 + 6*x + x^2)/((1 + x)*(1 - x)^2).
a(n) = a(n-1) + a(n-2) - a(n-3).
a(n) = 5*n - (3 - (-1)^n)/2.
a(n) = -A131229(-n+1) with A131229(0) = -3.
Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt((5+sqrt(5))/2)*Pi/10 - 3*log(phi)/(2*sqrt(5)), where phi is the golden ratio (A001622). - Amiram Eldar, Apr 15 2023

Extensions

Edited by Bruno Berselli, Jan 25 2016
Showing 1-4 of 4 results.

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