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 A224338 Number of idempotent 7 X 7 0..n matrices of rank 6. 1
 889, 10199, 57337, 218743, 653177, 1647079, 3670009, 7440167, 13999993, 24801847, 41803769, 67575319, 105413497, 159468743, 234881017, 337925959, 476171129, 658642327, 895999993, 1200725687, 1587318649, 2072502439, 2675441657 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Row 7 of A224333. LINKS R. H. Hardin, Table of n, a(n) for n = 1..210 Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1). FORMULA a(n) = 14*n^6 + 84*n^5 + 210*n^4 + 280*n^3 + 210*n^2 + 84*n + 7. 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 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 EXAMPLE Some solutions for n=1 ..1..0..0..0..0..0..0....1..0..0..0..0..0..0....1..0..0..1..0..0..0 ..0..1..0..0..0..0..0....0..1..0..0..0..1..0....0..1..0..0..0..0..0 ..0..0..1..0..0..0..0....0..0..1..0..0..1..0....0..0..1..0..0..0..0 ..0..0..0..0..0..1..1....0..0..0..1..0..0..0....0..0..0..0..0..0..0 ..0..0..0..0..1..0..0....0..0..0..0..1..1..0....0..0..0..1..1..0..0 ..0..0..0..0..0..1..0....0..0..0..0..0..0..0....0..0..0..0..0..1..0 ..0..0..0..0..0..0..1....0..0..0..0..0..1..1....0..0..0..1..0..0..1 PROG (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 CROSSREFS Cf. A224333. Sequence in context: A178270 A183751 A231954 * A250513 A252577 A202528 Adjacent sequences: A224335 A224336 A224337 * A224339 A224340 A224341 KEYWORD nonn,easy AUTHOR R. H. Hardin, formula via M. F. Hasler, William J. Keith, and Rob Pratt in the Sequence Fans Mailing List, Apr 03 2013 STATUS approved

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Last modified July 21 21:26 EDT 2024. Contains 374475 sequences. (Running on oeis4.)