OFFSET
1,1
COMMENTS
Row sums of triangle A193832. - Omar E. Pol, Aug 22 2011
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Zak Seidov Inside points
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = A186424(2*n-1).
By Pick's theorem, a(n) = 6*n^2 - 4*n + 1. - Nick Hobson, Mar 13 2007
O.g.f.: x*(3+8*x+x^2)/(1-x)^3 = -1 - 12/(-1+x)^3 - 11/(-1+x) - 22/(-1+x)^2. - R. J. Mathar, Dec 10 2007
E.g.f.: exp(x)*(1 + 2*x + 6*x^2) - 1. - Stefano Spezia, May 09 2021
EXAMPLE
At n=1, three lattice points (1,1), (1,2) and (2,1) are inside the triangle with vertices at the points (0,0), (3n,0) and (0,4n); hence a(1)=3.
MATHEMATICA
nip[a_, b_]:=Sum[Floor[b-b*i/a-10^-6], {i, a-1}] Table[nip[3k, 4k], {k, 100}]
Table[6*n^2-4*n+1, {n, 1, 50}] (* G. C. Greubel, Mar 06 2018 *)
PROG
(Magma) [6*n^2 - 4*n + 1: n in [1..50] ]; // Vincenzo Librandi, May 23 2011
(PARI) a(n)=6*n^2-4*n+1 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Zak Seidov, Jan 05 2007
STATUS
approved