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A224331 Number of idempotent n X n 0..6 matrices of rank n-1. 1
1, 26, 291, 2740, 24005, 201678, 1647079, 13176680, 103766409, 807072130, 6214455467, 47455841820, 359873467213, 2712892291382, 20346692185455, 151921968318160, 1129919639366417, 8374698503539434, 61879716720597043 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Column 6 of A224333.
LINKS
FORMULA
a(n) = n*(2*7^(n-1)-1).
a(n) = 16*a(n-1) - 78*a(n-2) + 112*a(n-3) - 49*a(n-4).
G.f.: x*(1 + 10*x - 47*x^2) / ((1 - x)^2*(1 - 7*x)^2). - Colin Barker, Aug 29 2018
EXAMPLE
Some solutions for n=3:
..1..5..0....0..3..6....1..0..0....0..0..0....1..0..0....1..0..0....0..0..0
..0..0..0....0..1..0....0..1..0....6..1..0....0..1..0....0..1..0....2..1..0
..0..2..1....0..0..1....0..0..0....4..0..1....1..6..0....3..4..0....3..0..1
MATHEMATICA
Table[n*(2*7^(n-1)-1), {n, 1, 40}] (* or *)
CoefficientList[Series[(1 + 10*x - 47*x^2) / ((1 - x)^2*(1 - 7*x)^2) , {x, 0, 40}], x] (* Stefano Spezia, Aug 29 2018 *)
PROG
(PARI) Vec(x*(1 + 10*x - 47*x^2) / ((1 - x)^2*(1 - 7*x)^2) + O(x^40)) \\ Colin Barker, Aug 29 2018
CROSSREFS
Cf. A224333.
Sequence in context: A336732 A227332 A020925 * A125414 A208600 A010831
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 April 22 18:11 EDT 2024. Contains 371906 sequences. (Running on oeis4.)