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
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
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