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A339609 Consider a triangle drawn on the perimeter of a triangular lattice with side length n. a(n) is the number of regions inside the triangle after drawing unit circles centered at each lattice point inside the triangle. 2
0, 0, 4, 10, 22, 39, 61, 88, 120, 157, 199, 246, 298, 355, 417, 484, 556, 633, 715, 802, 894, 991, 1093, 1200, 1312, 1429, 1551, 1678, 1810, 1947, 2089, 2236, 2388, 2545, 2707, 2874, 3046, 3223, 3405, 3592, 3784, 3981, 4183, 4390, 4602, 4819, 5041, 5268, 5500, 5737 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..50.

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

Peter Kagey, Example for a(4) = 10.

FORMULA

a(n) = (5*n^2 - 21*n + 24)/2 for n >= 4, with a(1)=a(2)=0, a(3)=4.

a(n) = A005476(n-2)+1 for n >= 4. - Hugo Pfoertner, Dec 10 2020

From Stefano Spezia, Dec 10 2020: (Start)

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

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n >= 4. (End)

MATHEMATICA

Join[{0, 0, 4}, Table[(5 n^2 - 21 n + 24)/2, {n, 4, 60}]]

CROSSREFS

Cf. A005476, A339623 (square version).

Sequence in context: A341734 A008255 A008031 * A008248 A301243 A177736

Adjacent sequences:  A339606 A339607 A339608 * A339610 A339611 A339612

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Dec 09 2020

STATUS

approved

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Last modified October 21 22:16 EDT 2021. Contains 348155 sequences. (Running on oeis4.)