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.

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A131876 2*A131873 - 1.

Original entry on oeis.org

1, 15, 7, 29, 15, 13, 43, 23, 21, 19, 57, 31, 29, 27, 25, 71, 39, 37, 35, 33, 31, 85, 47, 45, 43, 41, 39, 37, 99, 55, 53, 51, 49, 47, 45, 43, 113, 63, 61, 59, 57, 55, 53, 51, 49, 127, 71, 69, 67, 65, 63, 61, 59, 57, 55, 141, 79, 77, 75, 73, 71, 69, 67, 65, 63, 61, 155, 87, 85, 83, 81, 79, 77, 75, 73, 71, 69, 67, 169, 95, 93, 91, 89, 87, 85, 83, 81, 79, 77, 75, 73, 183, 103, 101, 99, 97, 95, 93, 91, 89, 87, 85, 83, 81, 79
Offset: 0

Views

Author

Gary W. Adamson, Jul 22 2007

Keywords

Comments

Left column = 14n + 1, A131877: (1, 15, 29, 43, 57, 21, ...).
Right border = 6n + 1, A016921: (1, 7, 13, 19, ...).
Row sums = A131878 (1, 22, 57, 106, 169, ...).

Examples

			First few rows of the triangle:
   1;
  15,  7;
  29, 15, 13;
  43, 23, 21, 19;
  57, 31, 29, 27, 25;
  71, 39, 37, 35, 33, 31;
  85, 47, 45, 43, 41, 39, 37;
  ...

Crossrefs

Cf. A131877, A131878, A131873.

Formula

2*A131873 - 1 as infinite lower triangular matrices.

Extensions

More terms from Russ Cox, Apr 18 2024

A131874 a(n) = (7*n^2 + 15*n + 2) / 2.

Original entry on oeis.org

1, 12, 30, 55, 87, 126, 172, 225, 285, 352, 426, 507, 595, 690, 792, 901, 1017, 1140, 1270, 1407, 1551, 1702, 1860, 2025, 2197, 2376, 2562, 2755, 2955, 3162, 3376, 3597, 3825, 4060, 4302, 4551, 4807, 5070, 5340, 5617, 5901, 6192, 6490, 6795, 7107, 7426
Offset: 0

Views

Author

Gary W. Adamson, Jul 22 2007

Keywords

Comments

Row sums of triangle A131873.

Examples

			a(2) = 30 = sum of row 2 terms of triangle A131873: (15 + 8 + 7).
a(2) = 30 = (1, 2, 1) dot (1, 11, 7) = (1 + 22 + 7).

Links

Crossrefs

Cf. A131873.

Programs

Formula

Binomial transform of (1, 11, 7, 0, 0, 0, ...).
a(n) = a(n-1) + 7*n + 4, (with a(0)=1). - Vincenzo Librandi, Nov 23 2010
a(n) = (2 + 15*n + 7*n^2)/2;
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3);
G.f.: (1 + 9*x - 3*x^2)/ (1-x)^3. - Colin Barker, Sep 13 2012

Extensions

More terms from Vladimir Joseph Stephan Orlovsky, Dec 04 2008
Showing 1-2 of 2 results.

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