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.

A134693 a(n)=A133806(n)+A133806(n+6).

Original entry on oeis.org

3, 9, 6, 18, 12, 36, 24, 72, 48, 144, 96, 288, 192, 576, 384, 1152, 768, 2304, 1536, 4608, 3072, 9216, 6144, 18432, 12288, 36864, 24576, 73728, 49152, 147456, 98304, 294912, 196608, 589824, 393216, 1179648, 786432, 2359296, 1572864, 4718592, 3145728
Offset: 0

Views

Author

Paul Curtz, Jan 27 2008

Keywords

Formula

a(n)=3*A074323(n+1).
a(2n)=A007283(n). a(2n+1)=3*A007283(n).
O.g.f.: 3(1+3x)/(1-2x^2). - R. J. Mathar, Jul 22 2008

Extensions

Edited and extended by R. J. Mathar, Jul 22 2008

A133805 Triangle read by rows: A007318 * A133566 * A133080.

Original entry on oeis.org

1, 2, 1, 4, 3, 1, 7, 6, 4, 1, 11, 10, 11, 5, 1, 16, 15, 25, 15, 6, 1, 22, 21, 50, 35, 22, 7, 1, 29, 28, 91, 70, 63, 28, 8, 1, 37, 36, 154, 126, 154, 84, 37, 9, 1, 46, 45, 246, 210, 336, 210, 129, 45, 10, 1, 56, 55, 375, 330, 672, 462, 375, 165, 56, 11, 1, 67, 66, 550, 495, 1254, 924, 957, 495, 231, 66, 12, 1
Offset: 1

Views

Author

Gary W. Adamson, Sep 23 2007

Keywords

Comments

Row sums = A133806: (1, 3, 8, 18, 38, 78, 318, ...).
Left column = A000124.

Examples

			First few rows of the triangle:
   1;
   2,  1;
   4,  3,  1;
   7,  6,  4,  1;
  11, 10, 11,  5,  1;
  16, 15, 25, 15,  6,  1;
  22, 21, 50, 35, 22,  7,  1;
  29, 28, 91, 70, 63, 28,  8,  1;
  ...

Crossrefs

Cf. A000124, A133080, A133566, A133804, A133806.

Formula

Binomial transform of (A133566 * A133080) where (A133566 * A133080) = an infinite lower triangular matrix with (1,1,1,...) in the main and subdiagonals and (1,0,1,0,1,...) in the subsubdiagonal.

Extensions

a(21) = 1 inserted and more terms from Georg Fischer, Jun 08 2023

A133807 A007318 * (A097806 + A133566 - I), where I is the identity matrix.

Original entry on oeis.org

1, 2, 1, 3, 4, 1, 4, 9, 4, 1, 5, 16, 10, 6, 1, 6, 25, 20, 20, 6, 1, 7, 36, 35, 50, 21, 8, 1, 8, 49, 56, 105, 56, 35, 8, 1, 9, 64, 84, 196, 126, 112, 36, 10, 1, 10, 81, 120, 336, 252, 294, 120, 54, 10, 1
Offset: 1

Views

Author

Gary W. Adamson, Sep 23 2007

Keywords

Comments

Row sums = A133806: (1, 3, 8, 18, 38, 78, 158, ...).

Examples

			First few rows of the triangle:
  1;
  2,  1;
  3,  4,  1;
  4,  9,  4,  1;
  5, 16, 10,  6,  1;
  6, 25, 20, 20,  6,  1;
  7, 36, 35, 50, 21,  8,  1;
  ...

Crossrefs

Cf. A133566, A007318 , A097806, A133806.

Formula

Binomial transform of matrix M, where M = (A097806 + A133566 - I) = triangle with (1,1,1,...) in the main diagonal, (1,2,1,2,1,...) in the subdiagonal and the rest zeros. I = Identity matrix.
Showing 1-3 of 3 results.

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

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