A192136 a(n) = (5*n^2 - 3*n + 2)/2.

1, 2, 8, 19, 35, 56, 82, 113, 149, 190, 236, 287, 343, 404, 470, 541, 617, 698, 784, 875, 971, 1072, 1178, 1289, 1405, 1526, 1652, 1783, 1919, 2060, 2206, 2357, 2513, 2674, 2840, 3011, 3187, 3368, 3554, 3745, 3941, 4142, 4348, 4559, 4775, 4996, 5222, 5453, 5689

Offset

0,2

Comments

Binomial transform of [1, 1, 5, 0, 0, 0, 0, 0, ...]. - Johannes W. Meijer, Jul 07 2011

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

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

Formula

a(n) = (5*n^2 - 3*n + 2)/2.

a(n) = 2*a(n-1) - a(n-2) + 5.

a(n) = a(n-1) + 5*n - 4.

a(n) = 5*binomial(n+2,2) - 9*n - 4.

a(n) = A000217(n+1) - A000217(n) + 5*A000217(n-1); triangular numbers. - Johannes W. Meijer, Jul 07 2011

O.g.f.: (1-x+5*x^2)/(1-x)^3.

From Elmo R. Oliveira, Nov 16 2024: (Start)

E.g.f.: exp(x)*(2 + 2*x + 5*x^2)/2.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)

Mathematica

Table[(5n^2-3n+2)/2, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 2, 8}, 50] (* Harvey P. Dale, Aug 08 2016 *)

Prog

(Magma) A192136:=func< n | (5*n^2-3*n+2)/2 >; [ A192136(n): n in [0..50] ]; // Klaus Brockhaus, Jun 27 2011
(PARI) a(n)=n*(5*n-3)/2+1 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A000124, A000217, A002522, A006137, A130883, A140063, A140064, A143689.

Sequence in context: A109071 A196134 A256321 * A031327 A193389 A030504

Adjacent sequences: A192133 A192134 A192135 * A192137 A192138 A192139

Keyword

nonn,easy

Author

Eric Werley, Jun 24 2011

Status

approved