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 1-5 of 5 results.

A131335 A000012 * A131334.

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 2, 2, 2, 1, 3, 2, 4, 2, 1, 3, 3, 6, 4, 3, 1, 4, 3, 9, 6, 7, 3, 1, 4, 4, 12, 9, 13, 7, 4, 1, 5, 4, 16, 12, 22, 13, 11, 4, 1, 5, 5, 20, 16, 34, 22, 24, 11, 5, 1
Offset: 1

Views

Author

Gary W. Adamson, Jun 29 2007

Keywords

Comments

Row sums = A000071, Fibonacci numbers - 1, starting (1, 2, 4, 7, 12, 20, 33,...).

Examples

			First few rows of the triangle are:
1;
1, 1;
2, 1, 1;
2, 2, 2, 1;
3, 2, 4, 2, 1;
3, 3, 6, 4, 3, 1;
4, 3, 9, 6, 7, 3, 1;
...

Crossrefs

Cf. A000071, A131334, A000012, A131332, A131333.

Formula

A000012 * A131334 as infinite lower triangular matrices, where A000012 = (1; 1,1; 1,1,1;...).

A131336 A131334 * A000012.

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 3, 3, 2, 1, 5, 4, 4, 2, 1, 8, 8, 7, 5, 3, 1, 13, 12, 12, 9, 7, 3, 1, 21, 21, 20, 17, 14, 8, 4, 1, 34, 33, 33, 29, 26, 17, 11, 4, 1, 55, 55, 54, 50, 46, 34, 25, 12, 5, 1
Offset: 1

Views

Author

Gary W. Adamson, Jun 29 2007

Keywords

Comments

Left border = Fibonacci numbers. Row sums = A131337.

Examples

			First few rows of the triangle are:
1;
1, 1;
2, 1, 1;
3, 3, 2, 1;
5, 4, 4, 2, 1;
8, 8, 7, 5, 3, 1;
13, 12, 12, 9, 7, 3, 1;
21, 21, 20 17, 14, 8, 4, 1;
...

Crossrefs

Cf. A131334, A131332, A131333, A131335, A131337.

Formula

A131334 * A000012, (partial row sums of A131334 starting from the right).

A131332 Triangle read by rows: A065941 * A097807.

Original entry on oeis.org

1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 2, -1, 2, 1, 1, 3, -2, 3, 1, 2, 1, 5, -4, 5, 0, 4, 2, 1, 8, -7, 8, -2, 7, 3, 3, 1, 13, -12, 13, -6, 12, 3, 7, 3, 1, 21, -20, 21, -13, 20, 1, 14, 6, 4, 1, 34, -33, 34, -25, 33, -5, 26, 9, 11, 4, 1, 55, -54, 55, -45, 54, -18, 46, 10, 25, 10, 5, 1, 89, -88, 89, -78, 88, -43, 79, 5, 51, 19, 16, 5, 1
Offset: 1

Views

Author

Gary W. Adamson, Jun 29 2007

Keywords

Comments

Row sums = Fibonacci numbers: (1, 1, 2, 3, 5, 8, ...).

Examples

			First few rows of the triangle are:
  1;
  0,  1;
  1,  0, 1;
  1,  0, 1,  1;
  2, -1, 2,  1, 1;
  3, -2, 3,  1, 2, 1;
  5, -4, 5,  0, 4, 2, 1;
  8, -7, 8, -2, 7, 3, 3, 1;
  ...

Crossrefs

Cf. A097807, A131333, A131334, A131335, A131336.

Formula

A065941 * A000012(signed by columns, + - + - ...).

Extensions

a(47) = -20 corrected, name edited and more terms from Georg Fischer, Jun 05 2023

A131333 A131332 * A000012.

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 3, 2, 2, 1, 5, 3, 4, 2, 1, 8, 5, 7, 4, 3, 1, 13, 8, 12, 7, 7, 3, 1, 21, 13, 20, 12, 14, 7, 4, 1, 34, 21, 33, 20, 26, 14, 11, 4, 1, 55, 34, 54, 33, 46, 26, 25, 11, 5, 1
Offset: 1

Views

Author

Gary W. Adamson, Jun 29 2007

Keywords

Comments

Leftmost two columns = Fibonacci numbers. Row sums = A029907: (1, 2, 4, 8, 15, 28, 51,...).

Examples

			First few rows of the triangle are:
1;
1, 1;
2, 1, 1;
3, 2, 2, 1;
5, 3, 4, 2, 1;
8, 5, 7, 4, 3, 1;
13, 8, 12, 7, 7, 3, 1;
21, 13, 20, 12, 14, 7, 4, 1;
...

Crossrefs

Cf. A131332, A131334, A131335, A131336.

Formula

A131332 * A000012, where A000012 = (1; 1,1; 1,1,1;...). Partial sums of A131332 rows starting from the right.

A131337 Row sums of triangle A131336.

Original entry on oeis.org

1, 2, 4, 9, 16, 32, 57, 106, 188, 337
Offset: 1

Views

Author

Gary W. Adamson, Jun 29 2007

Keywords

Examples

			a(4) = 9 = (3 + 3 + 2 + 2), sum of row 4, A131336.

Crossrefs

Cf. A131332, A131333, A131334, A131335, A131336.
Showing 1-5 of 5 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.