|
|
A255876
|
|
a(n) = (4*n^2 + 4*n - 3 - 3*(-1)^n)/2.
|
|
3
|
|
|
4, 9, 24, 37, 60, 81, 112, 141, 180, 217, 264, 309, 364, 417, 480, 541, 612, 681, 760, 837, 924, 1009, 1104, 1197, 1300, 1401, 1512, 1621, 1740, 1857, 1984, 2109, 2244, 2377, 2520, 2661, 2812, 2961, 3120, 3277, 3444, 3609, 3784, 3957, 4140, 4321, 4512, 4701
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Take an n X n square grid and add unit squares along each side except for the corners --> do this repeatedly along each side with the same restriction until no squares can be added. a(n) gives the number of vertices in each figure (see example and cf. A255840).
|
|
LINKS
|
|
|
FORMULA
|
G.f.: x*(3*x^3 - 6*x^2 - x - 4)/((x + 1)*(x - 1)^3).
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).
|
|
EXAMPLE
|
_
_|_|_
_ _ _ _|_|_|_|_
_|_|_ _|_|_|_ _|_|_|_|_|_|_
_ _ _|_|_|_|_ _|_|_|_|_|_ _|_|_|_|_|_|_|_|_
_ |_|_| |_|_|_|_|_| |_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_|
|_| |_|_| |_|_|_| |_|_|_|_|_|_| |_|_|_|_|_|_|_|
|_| |_|_|_|_| |_|_|_|_|_|
|_|_| |_|_|_|
|_|
n=1 n=2 n=3 n=4 n=5
|
|
MAPLE
|
|
|
MATHEMATICA
|
CoefficientList[Series[(3 x^3 - 6 x^2 - x - 4)/((x + 1) (x - 1)^3), {x, 0, 50}], x]
|
|
PROG
|
(Magma) [(4*n^2 + 4*n - 3 - 3*(-1)^n)/2 : n in [1..50]];
(PARI) vector(100, n, (4*n^2 + 4*n - 3 - 3*(-1)^n)/2) \\ Derek Orr, Mar 09 2015
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|