OFFSET
0,2
COMMENTS
Number of points in a square lattice enclosed by the four-pointed star figure with vertices at points (3n, 0), (n, n), (0, 3n), (-n, n), (-3n, 0), (-n, -n), (0, -3n), (n, -n).
Sequence found by reading the line from 1, in the direction 1, 17, ..., in the square spiral whose vertices are the generalized octagonal numbers A001082. - Omar E. Pol, Mar 06 2025
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
From Elmo R. Oliveira, Aug 21 2025: (Start)
G.f.: (1 + 14*x + 9*x^2)/(1 - x)^3.
E.g.f.: (1 + 16*x + 12*x^2)*exp(x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
EXAMPLE
Illustration of initial terms:
o
o
o o o
o o o o
o o o o o o
o o o o o o o o o o o o
o o o o o o o o o o o o o o o o o o o o o
o o o o o o o o o o o o
o o o o o o
o o o o
o o o
o
o
1 17 57
MATHEMATICA
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Aaron David Fairbanks, Mar 06 2025
STATUS
approved