OFFSET
0,2
COMMENTS
The associated r(n) are in A180509, which gives a combinatorial interpretation of the pairs (r(n),a(n)).
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,0,110,-110,0,0,-1,1).
FORMULA
G.f. ( -1-x-3*x^2-17*x^3+98*x^4-17*x^5-3*x^6-x^7-x^8 ) / ( (x-1)*(x^8-110*x^4+1) ). - R. J. Mathar, Feb 05 2011
Explicit formulas: r=sqrt(21), s=55+12*r, t=55-12*r:
a(4*n)=(42+(21+r)*s^n+(21-r)*t^n)/84.
a(4*n+1)=(42+(63+13*r)*s^n+(63-13*r)*t^n)/84.
a(4*n+2)=(42+(189+41*r)*s^n+(189-41*r)*t^n)/84.
a(4*n+3)=(42+(903+197*r)*s^n+(903-197*r)*t^n)/84.
a(n) = 111*a(n-4) - 111*a(n-8) + a(n-12).
a(n) = +a(n-1) +110*a(n-4) -110*a(n-5) -a(n-8) +a(n-9). - R. J. Mathar, Jan 05 2011
EXAMPLE
For n=2: a(2)=5; b(2)=26; binomial(26,7)=657800; binomial(26,5)*binomial(5,2)=657800.
MAPLE
n:=0: for s from 1 to 100 do r:=(sqrt(84*s^2-84*s+1)+11)/2: if (floor(r)=r) then a[n]:=s: b[n]:=r: n:=n+1: end if: end do:
MATHEMATICA
LinearRecurrence[{1, 0, 0, 110, -110, 0, 0, -1, 1}, {1, 2, 5, 22, 34, 161, 494, 2365, 3685}, 40] (* Harvey P. Dale, Aug 03 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul Weisenhorn, Jan 29 2011
STATUS
approved