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A084069 Numbers n such that 7*n^2 = floor(n*sqrt(7)*ceil(n*sqrt(7))). 3
1, 3, 17, 48, 271, 765, 4319, 12192, 68833, 194307, 1097009, 3096720, 17483311, 49353213, 278635967, 786554688, 4440692161, 12535521795, 70772438609, 199781794032, 1127918325583, 3183973182717, 17975920770719, 50743789129440 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..24.

Index entries for linear recurrences with constant coefficients, signature (0,16,0,-1).

FORMULA

a(1)=1, a(2)=3, a(2n)=6*a(2n-1)-a(2n-2); a(2n+1)=3*a(2n)-a(2n-1)

a(n)a(n+3) = -3 + a(n+1)a(n+2).

G.f.: x*(1+3*x+x^2)/(1-16*x^2+x^4).

a(n)=16*a(n-2)-a(n-4), n>4. [From Harvey P. Dale, Oct 31 2011]

MATHEMATICA

CoefficientList[Series[(1+3x+x^2)/(1-16x^2+x^4), {x, 0, 30}], x] (* or *) LinearRecurrence[{0, 16, 0, -1}, {1, 3, 17, 48}, 31] (* Harvey P. Dale, Oct 31 2011 *)

CROSSREFS

Cf. A159678, A001080, A001653, A001353, A060645, A001078, A001109, A084068, A084070.

Sequence in context: A095697 A154304 A144640 * A297514 A307862 A132124

Adjacent sequences:  A084066 A084067 A084068 * A084070 A084071 A084072

KEYWORD

nonn

AUTHOR

Benoit Cloitre, May 10 2003

EXTENSIONS

Corrected formula for generating function [Harvey P. Dale, Oct 31 2011]

STATUS

approved

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Last modified May 25 11:17 EDT 2019. Contains 323539 sequences. (Running on oeis4.)