A331190 Expansion of (-5*(9 - 6*x + 2*x^2))/(-1 + x)^3.

45, 105, 190, 300, 435, 595, 780, 990, 1225, 1485, 1770, 2080, 2415, 2775, 3160, 3570, 4005, 4465, 4950, 5460, 5995, 6555, 7140, 7750, 8385, 9045, 9730, 10440, 11175, 11935, 12720, 13530, 14365, 15225, 16110, 17020, 17955, 18915, 19900, 20910, 21945, 23005, 24090

Offset

0,1

Links

Table of n, a(n) for n=0..42.

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]LinearRecurrence[{3, -3, 1}, {45, 105, 190}, 50]

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

Sequence in context: A144552 A068355 A392495 * A332593 A144486 A376892

Adjacent sequences: A331187 A331188 A331189 * A331191 A331192 A331193

Keyword

nonn,easy

Author

Michael De Vlieger, Jan 11 2020

Status

approved