OFFSET
1,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,8,-8,-1,1).
FORMULA
a(n+4) = 8*a(n+2)-a(n)-27; r15=sqrt(15).
a(n) = ((1+r15)*(4+r15)^((n-1)/2)+(1-r15*(4-r15)^((n-1)/2)+18)/4 for n odd;
a(n) = ((11+3*r15)*(4+r15)^((n-2)/2)+(11-3*r15)*(4-r15)^((n-2)/2)+18)/4 for n even.
a(n) = a(n-1)+8*a(n-2)-8*a(n-3)-a(n-4)+a(n-5). G.f.: -x*(4*x^4-5*x^3-36*x^2+5*x+5) / ((x-1)*(x^4-8*x^2+1)). [Colin Barker, Jan 01 2013]
EXAMPLE
for n=4 a(4)=49; b(4)=12; binomial(49,6)=1383816;
binomial(49,4)*binomial(12,2)= 211876*66=1383816;
MAPLE
n:=1: for m from 1 to 2000 do w:=sqrt(1+60*m*(m-1)):
if (w=floor(w)) then a(n)=(9+w)/2: b(n):=m: inc(n): end if: end do:
CROSSREFS
KEYWORD
nonn,uned,easy
AUTHOR
Paul Weisenhorn, Jun 30 2010
EXTENSIONS
More terms from Colin Barker, Jan 01 2013
STATUS
approved