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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

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OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..34.

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

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

EXAMPLE

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

MATHEMATICA

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

CROSSREFS

Cf. A112259, A112260.

Sequence in context: A389338 A394550 A135169 * A021172 A094880 A351216

Adjacent sequences: A335837 A335838 A335839 * A335841 A335842 A335843

KEYWORD

nonn,easy

AUTHOR

Philippe Deléham, Sep 18 2020

STATUS

approved

URL: https://oeis.org/A335840

⇱ A335840 - OEIS