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

Author

A.K. Devaraj, Nov 05 2009

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A005476, A167467.

Similar sequences are listed in A316466.

Programs

GAP

List([1..50], n-> 3*n*(5*n-1)/2); # G. C. Greubel, Sep 01 2019

Magma

[3*n*(5*n-1)/2 : n in [1..50]]; // Wesley Ivan Hurt, May 08 2016

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 *)

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

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

Extensions

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

Name changed by Wesley Ivan Hurt, May 08 2016