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A224338 Number of idempotent 7 X 7 0..n matrices of rank 6.

%I A224338 #16 May 21 2021 15:50:54
%S A224338 889,10199,57337,218743,653177,1647079,3670009,7440167,13999993,
%T A224338 24801847,41803769,67575319,105413497,159468743,234881017,337925959,
%U A224338 476171129,658642327,895999993,1200725687,1587318649,2072502439,2675441657
%N A224338 Number of idempotent 7 X 7 0..n matrices of rank 6.
%C A224338 Row 7 of A224333.
%H A224338 R. H. Hardin, <a href="/A224338/b224338.txt">Table of n, a(n) for n = 1..210</a>
%H A224338 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A224338 a(n) = 14*n^6 + 84*n^5 + 210*n^4 + 280*n^3 + 210*n^2 + 84*n + 7.
%F A224338 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7). - _Colin Barker_, Sep 20 2014
%F A224338 G.f.: -7*x*(x^6-8*x^5+29*x^4+64*x^3+659*x^2+568*x+127) / (x-1)^7. - _Colin Barker_, Sep 20 2014
%e A224338 Some solutions for n=1
%e A224338 ..1..0..0..0..0..0..0....1..0..0..0..0..0..0....1..0..0..1..0..0..0
%e A224338 ..0..1..0..0..0..0..0....0..1..0..0..0..1..0....0..1..0..0..0..0..0
%e A224338 ..0..0..1..0..0..0..0....0..0..1..0..0..1..0....0..0..1..0..0..0..0
%e A224338 ..0..0..0..0..0..1..1....0..0..0..1..0..0..0....0..0..0..0..0..0..0
%e A224338 ..0..0..0..0..1..0..0....0..0..0..0..1..1..0....0..0..0..1..1..0..0
%e A224338 ..0..0..0..0..0..1..0....0..0..0..0..0..0..0....0..0..0..0..0..1..0
%e A224338 ..0..0..0..0..0..0..1....0..0..0..0..0..1..1....0..0..0..1..0..0..1
%o A224338 (PARI) Vec(-7*x*(x^6-8*x^5+29*x^4+64*x^3+659*x^2+568*x+127)/(x-1)^7 + O(x^100)) \\ _Colin Barker_, Sep 20 2014
%Y A224338 Cf. A224333.
%K A224338 nonn,easy
%O A224338 1,1
%A A224338 _R. H. Hardin_, formula via _M. F. Hasler_, _William J. Keith_, and _Rob Pratt_ in the Sequence Fans Mailing List, Apr 03 2013