OFFSET
1,2
COMMENTS
Sum_{i=1..infinity} 1/a(i) = 1.2758228304947598524736181699610...
LINKS
Bruno Berselli, Table of n, a(n) for n = 1..200
Index entries for linear recurrences with constant coefficients, signature (1,38,-38,-1,1)
FORMULA
G.f.: x*(1 + 3*x + 10*x^2 + 3*x^3 + x^4) / ((1 - x)*(1 - 38*x^2 + x^4)).
a(n) = a(n-1) + 38*a(n-2) - 38*a(n-3) - a(n-4) + a(n-5) for n>5, a(1)=1, a(2)=4, a(3)=52, a(4)=169, a(5)=1993.
a(n) = -1/2 + ( (15 + 4*sqrt(10)*(-1)^n)*(19 - 6*sqrt(10))^floor(n/2) + (15 - 4*sqrt(10)*(-1)^n)*(19 + 6*sqrt(10))^floor(n/2) )/20.
EXAMPLE
169 is in the sequence because 5*169*170/2-1 = 268^2.
MATHEMATICA
LinearRecurrence[{1, 38, -38, -1, 1}, {1, 4, 52, 169, 1993}, 30]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Dec 11 2013
STATUS
approved