OFFSET
0,2
COMMENTS
a(n-1) = n^k - 1 mod 2*n, n >= 1, for any k >= 2, also for k = n. - Wolfdieter Lang, Dec 21 2011
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).
FORMULA
G.f.: x*(x^2 + 2*x + 3)/(1 - x^2)^2. - Ralf Stephan, Jun 10 2003
Third main diagonal of A059026: a(n) = B(n+2, n) = lcm(n+2, n)/(n+2) + lcm(n+2, n)/n - 1 for all n >= 1.
a(2*n) + a(2*n+1) = A016945(n). - Paul Curtz, Aug 29 2008
E.g.f.: 2*x*cosh(x) + (1 + x)*sinh(x). - Franck Maminirina Ramaharo, Nov 08 2018
MAPLE
B := (n, m) -> lcm(n, m)/n + lcm(n, m)/m - 1: seq(B(m+2, m), m=1..90);
MATHEMATICA
Table[n +(n+1)*(1-(-1)^n)/2, {n, 0, 70}] (* G. C. Greubel, Nov 08 2018 *)
PROG
(PARI) a(n)=if(n%2, 2*n+1, n)
(Magma) [n+((n+1)/2)*(1-(-1)^n): n in [0..70]]; // Vincenzo Librandi, Aug 14 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Asher Auel, Dec 15 2000
EXTENSIONS
New description from Ralf Stephan, Jun 10 2003
STATUS
approved