OFFSET
0,1
LINKS
Amelia Carolina Sparavigna, The groupoid of the Triangular Numbers and the generation of related integer sequences, Politecnico di Torino, Italy (2019), see p. 4.
Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).
FORMULA
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 0, with a(0) = 0, a(1) = 45, a(2) = 105.
G.f.: (-5*(9 - 6*x + 2*x^2))/(-1 + x)^3.
MATHEMATICA
{0}~Join~LinearRecurrence[{3, -3, 1}, {45, 105, 190}, 43] (* or *)
CoefficientList[Series[(-5 (9 - 6 x + 2 x^2))/(-1 + x)^3, {x, 0, 42}], x]
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 45); Coefficients(R!( (-5*(9 - 6*x + 2*x^2))/(-1 + x)^3)); // Marius A. Burtea, Jan 11 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Michael De Vlieger, Jan 11 2020
STATUS
approved