A085293 Product of Lucas (A000204) and a Pell Companion series (A002203).

2, 18, 56, 238, 902, 3564, 13862, 54238, 211736, 827298, 3231362, 12623044, 49308482, 192613698, 752401496, 2939092798, 11480914982, 44847668844, 175187526662, 684331472398, 2673190054136, 10442227799538, 40790261396162, 159338166024964, 622419427368002

Offset

1,1

Comments

Convergent a(n+1)/a(n) = ((1+sqrt(5))/2)*(1+sqrt(2)) = (1.618...)*(2.414213...) = 3.9062796... = (1 + sqrt(2) + sqrt(5) + sqrt(10))/2.

Links

Table of n, a(n) for n=1..25.

Index entries for linear recurrences with constant coefficients, signature (2,7,2,-1).

Formula

a(n) = A000204(n) * A002203(n), n > 0.

a(n) = 2*A085292(n).

a(n) = (((1+sqrt(5))/2)^n + ((1-sqrt(5))/2)^n) * ((1+sqrt(2))^n + (1-sqrt(2))^n).

From Colin Barker, Oct 15 2013: (Start)

a(n) = 2*a(n-1) + 7*a(n-2) + 2*a(n-3) - a(n-4).

G.f.: -2*x*(2*x^3 - 3*x^2 - 7*x - 1) / (x^4 - 2*x^3 - 7*x^2 - 2*x + 1). (End)

E.g.f.: 4*(exp(x/2)*(cosh(x/sqrt(2))*cosh(sqrt(5/2)*x)*cosh(sqrt(5)*x/2)+sinh(x/sqrt(2))*sinh(sqrt(5/2)*x)*sinh(sqrt(5)*x/2))-1). - Stefano Spezia, Aug 25 2019

Prog

(Magma) I:=[2, 18, 56, 238]; [n le 4 select I[n] else 2*Self(n-1) + 7*Self(n-2) + 2*Self(n-3) - Self(n-4):n in [1..30]]; // Marius A. Burtea, Aug 25 2019

Crossrefs

Cf. A000204, A002203, A085292.

Sequence in context: A058653 A058794 A114109 * A119118 A213820 A078837

Adjacent sequences: A085290 A085291 A085292 * A085294 A085295 A085296

Keyword

nonn,easy

Author

Gary W. Adamson, Jun 24 2003

Extensions

More terms from David Wasserman, Jan 31 2005

More terms from Colin Barker, Oct 16 2013

Status

approved