cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A224331 Number of idempotent n X n 0..6 matrices of rank n-1.

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%I A224331 #11 Aug 29 2018 10:11:24
%S A224331 1,26,291,2740,24005,201678,1647079,13176680,103766409,807072130,
%T A224331 6214455467,47455841820,359873467213,2712892291382,20346692185455,
%U A224331 151921968318160,1129919639366417,8374698503539434,61879716720597043
%N A224331 Number of idempotent n X n 0..6 matrices of rank n-1.
%C A224331 Column 6 of A224333.
%H A224331 R. H. Hardin, <a href="/A224331/b224331.txt">Table of n, a(n) for n = 1..210</a>
%H A224331 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (16,-78,112,-49).
%F A224331 a(n) = n*(2*7^(n-1)-1).
%F A224331 a(n) = 16*a(n-1) - 78*a(n-2) + 112*a(n-3) - 49*a(n-4).
%F A224331 G.f.: x*(1 + 10*x - 47*x^2) / ((1 - x)^2*(1 - 7*x)^2). - _Colin Barker_, Aug 29 2018
%e A224331 Some solutions for n=3:
%e A224331 ..1..5..0....0..3..6....1..0..0....0..0..0....1..0..0....1..0..0....0..0..0
%e A224331 ..0..0..0....0..1..0....0..1..0....6..1..0....0..1..0....0..1..0....2..1..0
%e A224331 ..0..2..1....0..0..1....0..0..0....4..0..1....1..6..0....3..4..0....3..0..1
%t A224331 Table[n*(2*7^(n-1)-1), {n, 1, 40}] (* or *)
%t A224331 CoefficientList[Series[(1 + 10*x - 47*x^2) / ((1 - x)^2*(1 - 7*x)^2) , {x, 0, 40}], x] (* _Stefano Spezia_, Aug 29 2018 *)
%o A224331 (PARI) Vec(x*(1 + 10*x - 47*x^2) / ((1 - x)^2*(1 - 7*x)^2) + O(x^40)) \\ _Colin Barker_, Aug 29 2018
%Y A224331 Cf. A224333.
%K A224331 nonn,easy
%O A224331 1,2
%A A224331 _R. H. Hardin_, formula via _M. F. Hasler_ _William J. Keith_ and Rob Pratt in the Sequence Fans Mailing List, Apr 03 2013