

A224336


Number of idempotent 5X5 0..n matrices of rank 4.


1



155, 805, 2555, 6245, 12955, 24005, 40955, 65605, 99995, 146405, 207355, 285605, 384155, 506245, 655355, 835205, 1049755, 1303205, 1599995, 1944805, 2342555, 2798405, 3317755, 3906245, 4569755, 5314405, 6146555, 7072805, 8099995, 9235205
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OFFSET

1,1


COMMENTS

Row 5 of A224333.


LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210
Index entries for linear recurrences with constant coefficients, signature (5,10,10,5,1).


FORMULA

a(n) = 10*n^4 + 40*n^3 + 60*n^2 + 40*n + 5.
a(n) = 5*a(n1)  10*a(n2) + 10*a(n3)  5*a(n4) + a(n5).  Colin Barker, Sep 20 2014
G.f.: 5*x*(x^46*x^3+16*x^2+6*x+31) / (x1)^5.  Colin Barker, Sep 20 2014


EXAMPLE

Some solutions for n=3
..1..0..0..1..0....0..0..0..0..0....0..2..3..2..2....1..0..0..1..0
..0..1..0..1..0....1..1..0..0..0....0..1..0..0..0....0..1..0..2..0
..0..0..1..2..0....3..0..1..0..0....0..0..1..0..0....0..0..1..2..0
..0..0..0..0..0....2..0..0..1..0....0..0..0..1..0....0..0..0..0..0
..0..0..0..2..1....3..0..0..0..1....0..0..0..0..1....0..0..0..1..1


PROG

(PARI) Vec(5*x*(x^46*x^3+16*x^2+6*x+31)/(x1)^5 + O(x^100)) \\ Colin Barker, Sep 20 2014


CROSSREFS

Sequence in context: A129640 A028382 A250936 * A218328 A101535 A010086
Adjacent sequences: A224333 A224334 A224335 * A224337 A224338 A224339


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



