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 1-10 of 13 results. Next

A131843 Triangle read by rows: 2*A131821 - A000012.

Original entry on oeis.org

1, 3, 3, 5, 1, 5, 7, 1, 1, 7, 9, 1, 1, 1, 9, 11, 1, 1, 1, 1, 11, 13, 1, 1, 1, 1, 1, 13, 15, 1, 1, 1, 1, 1, 1, 15, 17, 1, 1, 1, 1, 1, 1, 1, 17, 19, 1, 1, 1, 1, 1, 1, 1, 1, 19, 21, 1, 1, 1, 1, 1, 1, 1, 1, 1, 21, 23, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 23, 25, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 25, 27, 1, 1, 1, 1, 1
Offset: 0

Views

Author

Gary W. Adamson, Jul 21 2007

Keywords

Comments

Row sums = 5*n + 1, A016861: (1, 6, 11, 16, 21, ...).

Examples

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

Links

Crossrefs

Cf. A016861, A131821.

Formula

2*A131821 - A000012 as an infinite lower triangular matrix. 2*n - 1, (1, 3, 5, 7, ...) as right and left borders, with the rest zeros.

Extensions

Corrected and edited by B. D. Swan (bdswan(AT)gmail.com), Dec 20 2008

A131844 3*A131821 - 2.

Original entry on oeis.org

1, 4, 4, 7, 1, 7, 10, 1, 1, 10, 13, 1, 1, 1, 13, 16, 1, 1, 1, 1, 16, 19, 1, 1, 1, 1, 1, 19, 22, 1, 1, 1, 1, 1, 1, 22, 25, 1, 1, 1, 1, 1, 1, 1, 25, 28, 1, 1, 1, 1, 1, 1, 1, 1, 28, 31, 1, 1, 1, 1, 1, 1, 1, 1, 1, 31, 34, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 34, 37, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 37, 40, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 40
Offset: 0

Views

Author

Gary W. Adamson, Jul 22 2007

Keywords

Comments

Row sums = A016993, (7n + 1): (1, 8, 15, 22, 29, ...).

Examples

			First few rows of the triangle:
   1;
   4,  4;
   7,  1,  7;
  10,  1,  1, 10;
  13,  1,  1,  1, 13;
  16,  1,  1,  1,  1, 16;
  ...

Crossrefs

Cf. A131821, A016993.

Formula

3*A131821 - 2 as infinite lower triangular matrices.
Infinite lower triangular matrix, (3n + 1): (1, 4, 7, 10, ...) as right and left borders and the rest 1's.

Extensions

More terms from Russ Cox, Apr 18 2024

A131897 A130321 + A131821 - A000012.

Original entry on oeis.org

1, 3, 2, 6, 2, 3, 11, 4, 2, 4, 20, 8, 4, 2, 5, 37, 16, 8, 4, 2, 6, 70, 32, 16, 8, 4, 2, 7, 135, 64, 32, 16, 8, 4, 2, 8, 264, 128, 64, 32, 16, 8, 4, 2, 9, 521, 256, 128, 64, 32, 16, 8, 4, 2, 10
Offset: 0

Views

Author

Gary W. Adamson, Jul 25 2007

Keywords

Comments

Left column = A006127: (1, 3, 6, 11, 20, 37, ...).
Row sums = A131898: (1, 5, 11, 21, 39, 73, ...).

Examples

			First few rows of the triangle:
   1;
   3,  2;
   6,  2,  3;
  11,  4,  2,  4;
  20,  8,  4,  2,  5;
  37, 16,  8,  4,  2,  6;
  70, 32, 16,  8,  4,  2,  7;
  ...

Crossrefs

Cf. A130321, A131821, A006127, A131898.

Formula

A131321 + A131821 - A000012 as infinite lower triangular matrices.

A131899 A002260 + A131821 - A000012.

Original entry on oeis.org

1, 2, 3, 3, 2, 5, 4, 2, 3, 7, 5, 2, 3, 4, 9, 6, 2, 3, 4, 5, 11, 7, 2, 3, 4, 5, 6, 13, 8, 2, 3, 4, 5, 6, 7, 15, 9, 2, 3, 4, 5, 6, 7, 8, 17, 10, 2, 3, 4, 5, 6, 7, 8, 9, 19
Offset: 0

Views

Author

Gary W. Adamson, Jul 25 2007

Keywords

Comments

Row sums = A052905: (1, 5, 10, 16, 23, ...)

Examples

			First few rows of the triangle:
  1;
  2,  3;
  3,  2,  5;
  4,  2,  3,  7;
  5,  2,  3,  4,  9;
  6,  2,  3,  4,  5, 11;
  7,  2,  3,  4,  5,  6, 13;
  ...

Crossrefs

Cf. A002260, A131821, A052905.

Formula

A002260 + A131821 - A000012 as infinite lower triangular matrices.

A131901 2*A002024 - A131821.

Original entry on oeis.org

1, 2, 2, 3, 5, 3, 4, 7, 7, 4, 5, 9, 9, 9, 5, 6, 11, 11, 11, 11, 6, 7, 13, 13, 13, 13, 13, 7, 8, 15, 15, 15, 15, 15, 15, 8, 9, 17, 17, 17, 17, 17, 17, 17, 9, 10, 19, 19, 19, 19, 19, 19, 19, 19, 10
Offset: 1

Views

Author

Gary W. Adamson, Jul 26 2007

Keywords

Comments

Row sums = A084849: (1, 4, 11, 22, 37, ...).

Examples

			First few rows of the triangle:
  1;
  2,  2;
  3,  5,  3;
  4,  7,  7,  4;
  5,  9,  9,  9,  5;
  6, 11, 11, 11, 11,  6;
  7, 13, 13, 13, 13, 13,  7;
  ...

Crossrefs

Cf. A002024, A131821, A084849.

Formula

2*A002024 - A131821 as infinite lower triangular matrices.

A131911 2*A131821 - A128174.

Original entry on oeis.org

1, 4, 3, 5, 2, 5, 8, 1, 2, 7, 9, 2, 1, 2, 9, 12, 1, 2, 1, 2, 11, 13, 2, 1, 2, 1, 2, 13, 16, 1, 2, 1, 2, 1, 2, 15, 17, 2, 1, 2, 1, 2, 1, 2, 17, 20, 1, 2, 1, 2, 1, 2, 1, 2, 19
Offset: 1

Views

Author

Gary W. Adamson, Jul 27 2007

Keywords

Comments

Left column, congruent to {0, 1} mod 4, A042948: (1, 4, 5, 8, 9, 12, 13, 16, ...).
Row sums = A131912: (1, 7, 12, 18, 23, 29, 34, ...).

Examples

			First few rows of the triangle:
   1;
   4,  3;
   5,  2,  5;
   8,  1,  2,  7;
   9,  2,  1,  2,  9;
  12,  1,  2,  1,  2, 11;
  13,  2,  1,  2,  1,  2, 13;
  ...

Crossrefs

Cf. A131821, A128174, A042948, A131912.

Formula

2*A131821 - A128174 as infinite lower triangular matrices.

A131950 A002024 + A131821 + A007318 - 2*A000012 as infinite lower triangular matrices.

Original entry on oeis.org

1, 3, 3, 5, 4, 5, 7, 6, 6, 7, 9, 8, 10, 8, 9, 11, 10, 15, 15, 10, 11, 13, 12, 21, 26, 21, 12, 13, 15, 14, 28, 42, 42, 28, 14, 15, 17, 16, 36, 64, 78, 64, 36, 16, 17, 19, 18, 45, 93, 135, 135, 93, 45, 18, 19
Offset: 0

Views

Author

Gary W. Adamson, Jul 30 2007

Keywords

Comments

Row sums = A131951: (1, 6, 14, 26, 44, 72, ...).

Examples

			First few rows of the triangle:
   1;
   3,  3;
   5,  4,  5;
   7,  6,  6,  7;
   9,  8, 10,  8,  9;
  11, 10, 15, 15, 10, 11;
  13, 12, 21, 26, 21, 12, 13;
  15, 14, 28, 42, 42, 28, 14, 15;
  ...

Crossrefs

Cf. A002024, A131821, A007318, A000012, A131951.

A132073 A007318 + A131821 - A103451 as infinite lower triangular matrices.

Original entry on oeis.org

1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 7, 5, 5, 6, 6, 11, 11, 6, 6, 7, 7, 16, 21, 16, 7, 7, 8, 8, 22, 36, 36, 22, 8, 8, 9, 9, 29, 57, 71, 57, 29, 9, 9, 10, 10, 37, 85, 127, 127, 85, 37, 10, 10
Offset: 0

Views

Author

Gary W. Adamson, Aug 09 2007

Keywords

Comments

Row sums = A132074: (1, 4, 9, 16, 27, 46, 81, 148, 279, ...).

Examples

			First few rows of the triangle:
   1;
   2,  2;
   3,  3,  3;
   4,  4,  4,  4;
   5,  5,  7,  5,   5;
   6,  6, 11, 11,   6,   6;
   7,  7, 16, 21,  16,   7,  7;
   8,  8, 22, 36,  36,  22,  8,  8;
   9,  9, 29, 57,  71,  57, 29,  9,  9;
  10, 10, 37, 85, 127, 127, 85, 37, 10, 10;
  ...

Crossrefs

Cf. A007318, A131821, A103451, A132074.

A131828 Square of lower triangular matrix in A131821, read by rows.

Original entry on oeis.org

1, 6, 4, 14, 5, 9, 25, 7, 7, 16, 39, 9, 9, 9, 25, 56, 11, 11, 11, 11, 36, 76, 13, 13, 13, 13, 13, 49, 99, 15, 15, 15, 15, 15, 15, 64, 125, 17, 17, 17, 17, 17, 17, 17, 81, 154, 19, 19, 19, 19, 19, 19, 19, 19, 100
Offset: 1

Views

Author

Gary W. Adamson, Jul 20 2007

Keywords

Comments

Left column = A095794: (1, 6, 14, 25, 39, 56, ...).
Row sums = A060544: (1, 10, 28, 55, 91, 190, ...).

Examples

			First few rows of the triangle:
   1;
   6,  4;
  14,  5,  9;
  25,  7,  7, 16;
  39,  9,  9,  9, 25;
  56, 11, 11, 11, 11, 36;
  76, 13, 13, 13, 13, 13, 49;
  ...

Crossrefs

Cf. A131821, A095794, A060544.

Formula

A131821^2.

A131900 A131821 + A128174 - A000012.

Original entry on oeis.org

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

Views

Author

Gary W. Adamson, Jul 25 2007

Keywords

Comments

Row sums = A047219, numbers congruent to {1, 3} (mod 5): (1, 3, 6, 8, 11, 13, ...).

Examples

			First few rows of the triangle:
  1;
  1, 2;
  3, 0, 3;
  3, 1, 0, 4;
  5, 0, 1, 0, 5;
  5, 1, 0, 1, 0, 6;
  7, 0, 1, 0, 1, 0, 7;
  ...

Crossrefs

Cf. A131821, A128174, A047219.

Formula

A131821 + A128174 - A000012 as infinite lower triangular matrices.
Showing 1-10 of 13 results. Next

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