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Segment Information (Details)
$ in Thousands
 3 Months Ended 6 Months Ended
Mar. 31, 2022
USD ($)
state
region
Mar. 31, 2021
USD ($)
Mar. 31, 2022
USD ($)
state
segment
region
Mar. 31, 2021
USD ($)
Sep. 30, 2021
USD ($)
Segment Reporting [Abstract]          
Number of states in which home building segments operate | state 13   13    
Number of regions in which entity operates | region 3   3    
Number of reportable segments | segment     3    
Segment Reporting Information [Line Items]          
Revenue $ 508,506 $ 549,889 $ 962,655 $ 978,428  
Operating income 54,611 33,618 95,550 51,306  
Depreciation and amortization 3,031 3,683 5,912 6,805  
Capital expenditures     6,195 6,514  
Assets 2,160,004   2,160,004   $ 2,078,810
Operating Segments          
Segment Reporting Information [Line Items]          
Operating income 92,182 80,011 162,965 134,990  
Depreciation and amortization 2,551 3,187 4,984 5,790  
Corporate and unallocated          
Segment Reporting Information [Line Items]          
Operating income (37,571) (46,393) (67,415) (83,684)  
Depreciation and amortization 480 496 928 1,015  
Capital expenditures     2,072 2,069  
Assets 598,900   598,900   676,779
West          
Segment Reporting Information [Line Items]          
Revenue 303,492 278,720 561,158 515,600  
West | Operating Segments          
Segment Reporting Information [Line Items]          
Operating income 58,103 42,488 100,827 75,791  
Depreciation and amortization 1,810 1,936 3,409 3,473  
Capital expenditures     3,275 3,066  
Assets 921,217   921,217   819,317
East          
Segment Reporting Information [Line Items]          
Revenue 128,935 153,571 247,104 251,535  
East | Operating Segments          
Segment Reporting Information [Line Items]          
Operating income 24,072 22,449 43,931 33,817  
Depreciation and amortization 367 575 802 1,046  
Capital expenditures     253 1,001  
Assets 314,973   314,973   286,133
Southeast          
Segment Reporting Information [Line Items]          
Revenue 76,079 117,598 154,393 211,293  
Southeast | Operating Segments          
Segment Reporting Information [Line Items]          
Operating income 10,007 15,074 18,207 25,382  
Depreciation and amortization 374 $ 676 773 1,271  
Capital expenditures     595 $ 378  
Assets $ 324,914   $ 324,914   $ 296,581