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A167469
a(n) = 3*n*(5*n-1)/2.
3
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
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
Similar sequences are listed in A316466.
Sequence in context: A012365 A217189 A363696 * A190623 A305158 A273408
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