OFFSET
0,1
COMMENTS
Gamma(a, x) is the upper incomplete Gamma function.
LINKS
Eric Weisstein's MathWorld, Incomplete Gamma Function, Golden Ratio.
FORMULA
E.g.f: (exp(phi*x) + exp((1-phi)*x))/(1-x).
Recurrence: n*(a(n) + a(n-1)) = (n+3)*a(n+1) - a(n+2).
a(n) ~ 2*exp(1/2)*cosh(sqrt(5)/2) * (n-1)!. - Vaclav Kotesovec, Oct 10 2016
MATHEMATICA
RecurrenceTable[{a[0] == 2, a[1] == 3, a[2] == 9, n (a[n] + a[n - 1]) == (n + 3) a[n + 1] - a[n + 2]}, a[n], {n, 0, 20}] (* or *)
Round@Table[Gamma[n + 1, GoldenRatio] Exp[GoldenRatio] + Gamma[n + 1, 1 - GoldenRatio] Exp[1 - GoldenRatio], {n, 0, 20}] (* Round is equivalent to FullSimplify here, but is much faster *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Reshetnikov, Oct 09 2016
STATUS
approved