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A224338 Number of idempotent 7X7 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

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 September 25 21:33 EDT 2017. Contains 292500 sequences.