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 1-2 of 2 results.

A131895 a(n) = (n + 2)*(5*n + 1)/2.

Original entry on oeis.org

1, 9, 22, 40, 63, 91, 124, 162, 205, 253, 306, 364, 427, 495, 568, 646, 729, 817, 910, 1008, 1111, 1219, 1332, 1450, 1573, 1701, 1834, 1972, 2115, 2263, 2416, 2574, 2737, 2905, 3078, 3256, 3439, 3627, 3820, 4018, 4221, 4429, 4642, 4860, 5083, 5311, 5544
Offset: 0

Views

Author

Gary W. Adamson, Jul 24 2007

Keywords

Comments

Row sums of triangle A131894.
Binomial transform of (1, 8, 5, 0, 0, 0, ...).

Examples

			a(2) = 22 = sum of row 2 terms of triangle A131894: (11 + 6 + 5).
a(2) = 22 = (1, 2, 1) dot (1, 8, 5) = (1 + 16 + 5).

Links

Crossrefs

Cf. A001622, A019952, A131894.

Programs

Formula

a(n) = a(n-1) + 5*n + 3 (with a(0)=1). - Vincenzo Librandi, Nov 23 2010
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(0)=1, a(1)=9, a(2)=22. - Harvey P. Dale, Sep 11 2015
From Elmo R. Oliveira, Oct 22 2024: (Start)
G.f.: (1 + 6*x - 2*x^2)/(1 - x)^3.
E.g.f.: (1 + 8*x + 5*x^2/2)*exp(x). (End)
Sum_{n>=0} 1/a(n) = (2 + sqrt(1+2/sqrt(5))*Pi + sqrt(5)*log(phi) + 5*log(5)/2)/9, where phi is the golden ratio (A001622). - Amiram Eldar, Jun 02 2025

Extensions

More terms from Vladimir Joseph Stephan Orlovsky, Dec 04 2008
Simpler definition from Wesley Ivan Hurt, Mar 26 2014

A131896 A000012 * A131843.

Original entry on oeis.org

1, 4, 3, 9, 4, 5, 16, 5, 6, 7, 25, 6, 7, 8, 9, 36, 7, 8, 9, 10, 11, 49, 8, 9, 10, 11, 12, 13, 64, 9, 10, 11, 12, 13, 14, 15, 81, 10, 11, 12, 13, 14, 15, 16, 17, 100, 11, 12, 13, 14, 15, 16, 17, 18, 19
Offset: 1

Views

Author

Gary W. Adamson, Jul 24 2007

Keywords

Comments

Row sums = A000566: (1, 7, 18, 34, 55, 81, ...), binomial transform of (1, 6, 5, 0, 0, 0, ...).
A131894 = A131843 * A000012.

Examples

			First few rows of the triangle:
   1;
   4,  3;
   9,  4,  5;
  16,  5,  6,  7;
  25,  6,  7,  8,  9;
  36,  7,  8,  9, 10, 11;
  49,  8,  9, 10, 11, 12, 13;
  64,  9, 10, 11, 12, 13, 14, 15;
  ...

Crossrefs

Cf. A131843, A000566.

Formula

A000012 * A131843 as infinite lower triangular matrices.
Showing 1-2 of 2 results.

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