OFFSET
0,3
COMMENTS
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (21,-175,735,-1624,1764,-720).
FORMULA
a(n)=sum(((-1)^j)*j^n,j=1..6)/3, n>=0.
E.g.f.: sum(((-1)^j)*exp(j*x),j=1..6)/3 = exp(x)*(exp(6*x)-1)/(3*(exp(x)+1)).
O.g.f.: sum(((-1)^j)/(1-j*x),j=1..6)/3 = x*(1-14*x+73*x^2-168*x^3+148*x^4)/
product(1-j*x,j=1..6). See A196847 for a formula for the coefficients of the numerator polynomial.
MAPLE
A198629 := proc(n)
(-3^n+4^n-1+2^n-5^n+6^n)/3 ;
end proc:
seq(A198629(n), n=0..20) ; # R. J. Mathar, May 11 2022
MATHEMATICA
Table[Total[Times@@@Partition[Riffle[Range[6]^n, {-1, 1}, {2, -1, 2}], 2]]/3, {n, 0, 30}] (* Harvey P. Dale, Jul 17 2016 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Oct 28 2011
STATUS
approved