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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.
3
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
OFFSET
1,2
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.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n >= 3. (End)
MATHEMATICA
Join[{1, 5}, LinearRecurrence[{3, -3, 1}, {21, 52, 97}, 49]] (* Amiram Eldar, Dec 10 2020 *)
PROG
(Magma) [1, 5] cat [7*n^2-18*n+12 : n in [3..80]];
CROSSREFS
Cf. A186862, A339609 (triangular version).
Sequence in context: A039659 A147238 A316435 * A272013 A219219 A272810
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Dec 10 2020
STATUS
approved