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.

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

Adjacent sequences: A339620 A339621 A339622 * A339624 A339625 A339626

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Dec 10 2020

STATUS

approved

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