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

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

0,2

Comments

Row sums of triangle A131894.

Binomial transform of (1, 8, 5, 0, 0, 0, ...).

Links

Table of n, a(n) for n=0..46.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

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

Example

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).

Maple

A131895:=n->(n+2)*(5*n+1)/2; seq(A131895(n), n=0..50); # Wesley Ivan Hurt, Mar 26 2014

Mathematica

LinearRecurrence[{3, -3, 1}, {1, 9, 22}, 50] (* Harvey P. Dale, Sep 11 2015 *)

Prog

(PARI) a(n)=(n+2)*(5*n+1)/2 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A001622, A019952, A131894.

Sequence in context: A154528 A130861 A049730 * A323221 A250730 A251285

Adjacent sequences: A131892 A131893 A131894 * A131896 A131897 A131898

Keyword

nonn,easy

Author

Gary W. Adamson, Jul 24 2007

Extensions

More terms from Vladimir Joseph Stephan Orlovsky, Dec 04 2008

Simpler definition from Wesley Ivan Hurt, Mar 26 2014

Status

approved