OFFSET
1,3
COMMENTS
Also, numbers m such that m*(m+1)*(m+2)*(m+3)*(m+4)/(m+(m+1)+(m+2)+(m+3)+(m+4)) is an integer.
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
FORMULA
a(n) = (1/8)*(10*n-11+(-1)^n+2*(-1)^floor(n/2)). - Ralf Stephan, Jun 09 2005
a(n) = floor((5*n-4)/4). - Gary Detlefs, Mar 06 2010
G.f.: x^2*(1+x+2*x^2+x^3) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011
From Wesley Ivan Hurt, May 30 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(n) = (10*n-11+i^(2*n)+(1+i)*I^(-n)+(1-i)*i^n)/8 where i=sqrt(-1).
E.g.f.: (4 + sin(x) + cos(x) + (5*x - 6)*sinh(x) + 5*(x - 1)*cosh(x))/4. - Ilya Gutkovskiy, May 31 2016
Sum_{n>=2} (-1)^n/a(n) = log(5)/4 + 3*sqrt(5)*log(phi)/10 - sqrt(1-2/sqrt(5))*Pi/10, where phi is the golden ratio (A001622). - Amiram Eldar, Dec 10 2021
MAPLE
seq(floor((5*n-4)/4), n=1..69); # Gary Detlefs, Mar 06 2010
MATHEMATICA
Table[Floor[(5n - 4)/4], {n, 80}] (* Wesley Ivan Hurt, May 30 2016 *)
PROG
(Magma) [Floor((5*n - 4)/4) : n in [1..80]]; // Wesley Ivan Hurt, May 30 2016
(PARI) a(n)=5*n\4-1 \\ Charles R Greathouse IV, Jan 02 2025
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Patrick De Geest, May 15 1998
EXTENSIONS
Better description from Michael Somos, Jun 08 2000
STATUS
approved