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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
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
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.)