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A105045 a(0)=0, a(1)=1, a(2)=2, a(3)=3, a(4)=12; for n > 4, a(n) = 8*a(n-2) - a(n-4) - 3. 4
0, 1, 2, 3, 12, 20, 91, 154, 713, 1209, 5610, 9515, 44164, 74908, 347699, 589746, 2737425, 4643057, 21551698, 36554707, 169676156, 287794596, 1335857547, 2265802058, 10517184217, 17838621865, 82801616186, 140443172859, 651895745268, 1105706761004, 5132364345955 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

It appears that this sequence gives all nonnegative m such that 60*m^2 - 60*m + 1 is a square and that for n > 3, a(n+1) = A103200(n) + 1.

From Paul Weisenhorn, Jun 30 2010: (Start)

b(n) red and a(n) blue balls in an urn; draw 6 balls without replacement;

binomial(b(n),6) = binomial(b(n),4)*binomial(a(n),2), where b(n)=A179123(n).

(End)

LINKS

Muniru A Asiru, Table of n, a(n) for n = 0..2000

Index entries for linear recurrences with constant coefficients, signature (1,8,-8,-1,1).

FORMULA

From Paul Weisenhorn, Jun 30 2010: (Start)

r=sqrt(15);

a(n)=((15+r)*(4+r)^((n-1)/2)+(15-r)*(4-r)^((n-1)/2)+30)/60; n odd

a(n)=((45+11*r)*(4+r)^((n-2)/2)+(45-11*r)*(4-r)^((n-2)/2)+30)/60; n even

(End)

a(n) = a(n-1) + 8*a(n-2) - 8*a(n-3) - a(n-4) + a(n-5); a(0)=0, a(1)=1, a(2)=2, a(3)=3, a(4)=12, a(5)=20. - Harvey P. Dale, Nov 10 2011

G.f.: -x*(x^4 + x^3 - 7*x^2 + x + 1) / ((x-1)*(x^4-8*x^2+1)). - Colin Barker, Jan 01 2013

EXAMPLE

For n=3, a(3)=3; b(3)=14; binomial(14,6)=3003; binomial(14,4)*binomial(3,2) = 1001*3 = 3003. - Paul Weisenhorn, Jun 30 2010

MAPLE

n:=1: for m from 1 to 2000 do w:=sqrt(1+60*m*(m-1)):

if (w=floor(w)) then a(n)=m: b(n)=(9+w)/2: inc(n): end if: end do # Paul Weisenhorn, Jun 30 2010

MATHEMATICA

Join[{0}, RecurrenceTable[{a[1]==1, a[2]==2, a[3]==3, a[4]==12, a[n] == 8a[n-2]-a[n-4]-3}, a, {n, 30}]] (* or *) Join[{0}, LinearRecurrence[ {1, 8, -8, -1, 1}, {1, 2, 3, 12, 20}, 30]] (* Harvey P. Dale, Nov 10 2011 *)

CROSSREFS

Cf. A103200, A001090.

Sequence in context: A083265 A067391 A096361 * A205825 A076000 A096632

Adjacent sequences:  A105042 A105043 A105044 * A105046 A105047 A105048

KEYWORD

nonn,easy

AUTHOR

Gerald McGarvey, Apr 03 2005

EXTENSIONS

More terms from Colin Barker, Jan 01 2013

STATUS

approved

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Last modified August 23 14:20 EDT 2019. Contains 326247 sequences. (Running on oeis4.)