A339623 - OEIS

A339623

Consider a square drawn on the perimeter of a square lattice with side length n. a(n) is the number of regions inside the square after drawing unit circles centered at each interior lattice point of the square.

1, 5, 21, 52, 97, 156, 229, 316, 417, 532, 661, 804, 961, 1132, 1317, 1516, 1729, 1956, 2197, 2452, 2721, 3004, 3301, 3612, 3937, 4276, 4629, 4996, 5377, 5772, 6181, 6604, 7041, 7492, 7957, 8436, 8929, 9436, 9957, 10492, 11041, 11604, 12181, 12772, 13377, 13996, 14629, 15276, 15937, 16612, 17301

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..51.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Peter Kagey, Example of a(4) = 52.

FORMULA

a(n) = 7*n^2 - 18*n + 12 for n >= 3, with a(1) = 1, a(2) = 5.

a(n) = A186862(n)/8+1 for n >= 3. - Hugo Pfoertner, Dec 10 2020

From Stefano Spezia, Dec 10 2020: (Start)

G.f.: x*(1 + 2*x + 9*x^2 + 3*x^3 - x^4)/(1 - x)^3.