%I #27 Sep 08 2022 08:45:48

%S 6,27,63,114,180,261,357,468,594,735,891,1062,1248,1449,1665,1896,

%T 2142,2403,2679,2970,3276,3597,3933,4284,4650,5031,5427,5838,6264,

%U 6705,7161,7632,8118,8619,9135,9666,10212,10773,11349,11940,12546,13167,13803,14454

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

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

%C Old name was: 3*A005476(n).

%C Sum of the numbers from n to 4*n-1 for n>=1. - _Wesley Ivan Hurt_, May 08 2016

%H G. C. Greubel, <a href="/A167469/b167469.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

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

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

%F a(n) = Sum_{i=n..4*n-1} i. - _Wesley Ivan Hurt_, May 08 2016

%F E.g.f.: 3*x*(4 + 5*x)*exp(x)/2. - _Ilya Gutkovskiy_, May 14 2016

%F 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

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

%t Table[3n(5n-1)/2, {n, 50}] (* _Vladimir Joseph Stephan Orlovsky_, Jul 06 2011 *)

%o (Magma) [3*n*(5*n-1)/2 : n in [1..50]]; // _Wesley Ivan Hurt_, May 08 2016

%o (PARI) x='x+O('x^50); Vec(3*x*(2+3*x)/(1-x)^3) \\ _Altug Alkan_, May 14 2016

%o (Sage) [3*n*(5*n-1)/2 for n in (1..50)] # _G. C. Greubel_, Sep 01 2019

%o (GAP) List([1..50], n-> 3*n*(5*n-1)/2); # _G. C. Greubel_, Sep 01 2019

%Y Cf. A005476, A167467.

%Y Similar sequences are listed in A316466.

%K nonn,easy

%O 1,1

%A _A.K. Devaraj_, Nov 05 2009

%E a(1) corrected, definition simplified, sequence extended by _R. J. Mathar_, Nov 12 2009

%E Name changed by _Wesley Ivan Hurt_, May 08 2016