OFFSET
0,2
COMMENTS
a(n) is the number of lattice points (x,y) in the coordinate plane bounded by y < 3x, y >= x/2 and x <= n.
a(n)+1 is the number of lattice points bounded by y <= 3x, y >= x/2 and x <= n.
LINKS
Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).
FORMULA
G.f.: x*(2+3*x)/((1-x)^3*(1+x)).
a(n) = 2*a(n-1)-2*a(n-3)+a(n-4) for n>3.
a(n) = Sum_{i=0..n} A001068(2*i). - Wesley Ivan Hurt, May 06 2016
E.g.f.: (x*(9 + 5*x)*exp(x) - sinh(x))/4. - Ilya Gutkovskiy, May 06 2016
MATHEMATICA
Table[(10*n^2 + 8 n - 1 + (-1)^n)/8 , {n, 0, 50}]
PROG
(Magma) [(10*n^2+8*n-1+(-1)^n)/8 : n in [0..50]];
(PARI) a(n) = (10*n^2+8*n-1+(-1)^n)/8; \\ Michel Marcus, Nov 04 2014
(PARI) concat(0, Vec(x*(2+3*x)/((1-x)^3*(1+x)) + O(x^100))) \\ Altug Alkan, Oct 28 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Oct 31 2014
STATUS
approved