OFFSET
1,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = (1/6)*(19*n^3-15*n^2+2*n). [Corrected by Luca Colucci, Mar 01 2011]
G.f.: x*(1 + 12*x + 6*x^2)/(1 - x)^4. - Colin Barker, Jun 08 2012
a(n) = Sum_{i = 0..n-1} (n + i)*(n + 2*i). - Bruno Berselli, Feb 14 2018
E.g.f.: exp(x)*x*(6 + 42*x + 19*x^2)/6. - Stefano Spezia, Oct 11 2023
MAPLE
a:=n->(1/6)*(19*n^3-15*n^2+2*n): seq(a(n), n=1..33); # Muniru A Asiru, Feb 14 2018
MATHEMATICA
Rest@ CoefficientList[Series[x (1 + 12 x + 6 x^2)/(1 - x)^4, {x, 0, 32}], x] (* Michael De Vlieger, Feb 15 2018 *)
PROG
(Magma) [(1/6)*(19*n^3-15*n^2+2*n): n in [1..40]]; // Vincenzo Librandi, Aug 18 2011
(GAP) List([1..33], n -> (1/6)*(19*n^3-15*n^2+2*n)); # Muniru A Asiru, Feb 14 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
James A. Record (james.record(AT)gmail.com), Nov 07 2004
STATUS
approved