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A181442 Solutions a(n) to (r(n)-2)*(r(n)-3) = 6*a(n)*(a(n)-1). 5
1, 2, 4, 15, 35, 144, 342, 1421, 3381, 14062, 33464, 139195, 331255, 1377884, 3279082, 13639641, 32459561, 135018522, 321316524, 1336545575, 3180705675, 13230437224, 31485740222, 130967826661, 311676696541, 1296447829382, 3085281225184, 12833510467155 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A combinatorial interpretation is provided in A180483, which also lists the r(n).

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,10,-10,-1,1).

FORMULA

G.f. ( -1-x+8*x^2-x^3-x^4 ) / ( (x-1)*(x^4-10*x^2+1) ). - R. J. Mathar, Feb 05 2011

Explicit formulas: r=sqrt(6), s=5+2*r, t=5-2*r.

a(2*n)=(12+(6+r)*s^n+(6-r)*t^n)/24.

a(2*n+1)=(12+(18+7*r)*s^n+(18-7*r)*t^n)/24.

a(n)=11*a(n-2)-11*a(n-4)+a(n-6).

a(n) = +a(n-1) +10*a(n-2) -10*a(n-3) -a(n-4) +a(n-5).

EXAMPLE

For n=3: a(3)=15; b(3)=38; binomial(38,4)=73815

binomial(38,2)*binomial(15,2)=73815

MAPLE

n:=0: for s from 1 to 100 do r:=(sqrt(24*s^2-24*s+1)+5)/2: if (floor(r)=r) then a[n]:=s: b[n]:=r: n:=n+1: end if: end do:

MATHEMATICA

LinearRecurrence[{1, 10, -10, -1, 1}, {1, 2, 4, 15, 35}, 30] (* Harvey P. Dale, Dec 22 2012 *)

CROSSREFS

Cf. A180483.

Sequence in context: A080623 A196260 A073814 * A007122 A005219 A153945

Adjacent sequences:  A181439 A181440 A181441 * A181443 A181444 A181445

KEYWORD

nonn

AUTHOR

Paul Weisenhorn, Jan 29 2011

STATUS

approved

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Last modified December 11 15:43 EST 2017. Contains 295905 sequences.