A335840 Expansion of x*(1+2*x)/((1-2*x)*(1-x+4*x^2)).

1, 5, 9, 5, 1, 45, 169, 245, 81, 125, 1849, 5445, 6241, 845, 8649, 70805, 167281, 146205, 1369, 465125, 2556801, 4890605, 3052009, 266805, 21613201, 87654845, 135419769, 53235845, 48427681, 909226125, 2862999049, 3521061845, 659000241, 3754622045

Offset: 1

Author

Philippe Deléham, Sep 18 2020

Keywords

• nonn
• easy

Comments

Numbers in the sequence are alternatively products of squares or five times a product of squares.

Examples

			a(11) = 43^2, a(12) = 5*3^2*11^2.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-6,8).

Crossrefs

Cf. A112259, A112260.

Programs

Mathematica

LinearRecurrence[{3,-6,8},{1,5,9},34] (* Stefano Spezia, Sep 19 2020 *)

Formula

G.f.: x*(1+2*x)/((1-2*x)*(1-x+4*x^2)).

a(n) = 3*a(n-1) - 6*a(n-2) + 8*a(n-3) for n > 3.

a(n) = A112259(n)/(A112260(n))^2.

3*a(n) = 2^(n+1) - A272931(n). - R. J. Mathar, Aug 19 2022