OFFSET
0,2
COMMENTS
y-values solving the Diophantine equation 4*x^3 + 9*x^2 = y^2 for positive x (which are listed in A028552). The equation is also satisfied by y=2 and x=-2.
LINKS
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
G.f.: 2*x*(10 - 5*x + x^2) / (1 - x)^4.
a(n) = n*(2*n^2 + 9*n + 9) = n * A014107(n+3).
MATHEMATICA
Table[2 n^3 + 9 n^2 + 9 n, {n, 0, 40}] (* or *) CoefficientList[Series[(20 x - 10 x^2 + 2 x^3) / (1 - x)^4, {x, 0, 33}], x]
PROG
(Magma) [2*n^3+9*n^2+9*n: n in [0..40]]
(GAP) List([0..50], n->n*(2*n^2+9*n+9)); # Muniru A Asiru, Apr 29 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Apr 28 2018
STATUS
approved