A167469 a(n) = 3*n*(5*n-1)/2.

6, 27, 63, 114, 180, 261, 357, 468, 594, 735, 891, 1062, 1248, 1449, 1665, 1896, 2142, 2403, 2679, 2970, 3276, 3597, 3933, 4284, 4650, 5031, 5427, 5838, 6264, 6705, 7161, 7632, 8118, 8619, 9135, 9666, 10212, 10773, 11349, 11940, 12546, 13167, 13803, 14454

Offset

1,1

Comments

This represents the nontrivial imaginary part of the decomposition of the trivariate rational polynomial described in A167467.

Old name was: 3*A005476(n).

Sum of the numbers from n to 4*n-1 for n>=1. - Wesley Ivan Hurt, May 08 2016

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

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

Formula

G.f.: 3*x*(2+3*x)/(1-x)^3.

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

a(n) = Sum_{i=n..4*n-1} i. - Wesley Ivan Hurt, May 08 2016

E.g.f.: 3*x*(4 + 5*x)*exp(x)/2. - Ilya Gutkovskiy, May 14 2016

a(n) = Sum_{i = 2..7} P(i,n), where P(i,m) = m*((i-2)*m-(i-4))/2. - Bruno Berselli, Jul 04 2018

Maple

A167469:=n->3*n*(5*n-1)/2: seq(A167469(n), n=1..50); # Wesley Ivan Hurt, May 08 2016

Mathematica

Table[3n(5n-1)/2, {n, 50}] (* Vladimir Joseph Stephan Orlovsky, Jul 06 2011 *)

Prog

(Magma) [3*n*(5*n-1)/2 : n in [1..50]]; // Wesley Ivan Hurt, May 08 2016
(PARI) x='x+O('x^50); Vec(3*x*(2+3*x)/(1-x)^3) \\ Altug Alkan, May 14 2016
(Sage) [3*n*(5*n-1)/2 for n in (1..50)] # G. C. Greubel, Sep 01 2019
(GAP) List([1..50], n-> 3*n*(5*n-1)/2); # G. C. Greubel, Sep 01 2019

Crossrefs

Cf. A005476, A167467.

Similar sequences are listed in A316466.

Sequence in context: A012365 A217189 A363696 * A190623 A305158 A273408

Adjacent sequences: A167466 A167467 A167468 * A167470 A167471 A167472

Keyword

nonn,easy

Author

A.K. Devaraj, Nov 05 2009

Extensions

a(1) corrected, definition simplified, sequence extended by R. J. Mathar, Nov 12 2009

Name changed by Wesley Ivan Hurt, May 08 2016

Status

approved