OFFSET
1,1
COMMENTS
When the numbers k*sinh[1/k] - 1 and 1 - k*sin[1/k], for k >=1, are jointly ranked, the former occupy positions 1,3,5,7,... and the latter occupy positions 2,4,6,8,... The difference between neighbors is n*Sinh[1/n] + n*Sin[1/n] - 2, so that A248968 represents the closeness between neighbors. All the terms end in 9.
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = 60*n^4 - 1.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - Colin Barker, Oct 22 2014
G.f.: x*(x^4-64*x^3-654*x^2-664*x-59) / (x-1)^5. - Colin Barker, Oct 22 2014
MATHEMATICA
Table[Floor[1/(n*Sinh[1/n] + n*Sin[1/n] - 2)], {n, 1, 60}]
PROG
(PARI) Vec(x*(x^4-64*x^3-654*x^2-664*x-59)/(x-1)^5 + O(x^100)) \\ Colin Barker, Oct 22 2014
(Magma) [Floor(1/(n*Sinh(1/n) + n*Sin(1/n) - 2)): n in [1..30]]; // Vincenzo Librandi, Oct 23 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 19 2014
STATUS
approved