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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
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).
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).
a(n) = A000290(n+1) + 4*A198442(n).
EXAMPLE
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n=1 n=2 n=3 n=4 n=5
MAPLE
A255876:=n->(4*n^2 + 4*n - 3 - 3*(-1)^n)/2: seq(A255876(n), n=1..50);
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
Cf. A000290 (squares), A085046, A198442, A255840.
Sequence in context: A288103 A286729 A159068 * A158141 A056575 A056032
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Mar 08 2015
STATUS
approved