OFFSET
4,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 4..10000
Index entries for linear recurrences with constant coefficients, signature (4,-5,0,5,-4,1).
FORMULA
G.f.: x^4*(2+x)/((1+x)*(1-x)^5).
a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - a(n-5) + 3. If sequence is also defined for n <= 3 by this equation, then a(n)=0 for 0 <= n <= 3 and a(n) = A070893(-n) for n < 0.
a(n) = A082290(2*n-7).
a(n) = (1/96)*(2*(n-2)*n*(3*n^2 - 10*n + 4) + 3*(-1)^n - 3). a(n) - a(n-2) = A006002(n-3) for n > 5. - Bruno Berselli, Aug 26 2011
a(n) = 4*a(n-1) - 5*a(n-2) + 5*a(n-4) - 4*a(n-5) + a(n-6); a(4)=2, a(5)=9, a(6)=26, a(7)=59, a(8)=116, a(9)=206. - Harvey P. Dale, Aug 26 2013
MATHEMATICA
Drop[CoefficientList[Series[x^4(2+x)/((1+x)(1-x)^5), {x, 0, 50}], x], 4] (* or *) LinearRecurrence[{4, -5, 0, 5, -4, 1}, {2, 9, 26, 59, 116, 206}, 50] (* Harvey P. Dale, Aug 26 2013 *)
PROG
(PARI) a(n)=polcoeff(if(n>0, x^4*(2+x)/((1+x)*(1-x)^5), x*(1+2*x)/((1+x)*(1-x)^5))+x*O(x^abs(n)), abs(n))
(Magma) [(1/96)*(2*(n-2)*n*(3*n^2-10*n+4)+3*(-1)^n-3): n in [4..50]]; // Vincenzo Librandi, Aug 29 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Michael Somos, Apr 07 2003
STATUS
approved