A381847 - OEIS

A381847

Number of 3 element sets of distinct integer sided rectangles that fill an n X n square.

0, 0, 2, 3, 8, 11, 19, 23, 35, 40, 55, 62, 80, 88, 110, 119, 144, 155, 183, 195, 227, 240, 275, 290, 328, 344, 386, 403, 448, 467, 515, 535, 587, 608, 663, 686, 744, 768, 830, 855, 920, 947, 1015, 1043, 1115, 1144, 1219, 1250, 1328, 1360, 1442, 1475, 1560

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OFFSET

1,3

LINKS

Table of n, a(n) for n=1..53.

Sean A. Irvine, Java program (github)

Index entries for linear recurrences with constant coefficients, signature (0,2,1,-1,-2,0,1).

FORMULA

G.f.: x^3*(2+3*x+4*x^2+3*x^3+2*x^4)/((1+x+x^2)*(1+x)^2*(1-x)^3). - Jinyuan Wang, Aug 03 2025

EXAMPLE

The a(3) = 2 sets of integer sided rectanges are:

{(3 X 2), (2 X 1), (1 X 1)},