(MAGMAMagma) I:=[1, 3, 13]; [n le 3 select I[n] else 7*Self(n-1)-3*Self(n-2)+5*Self(n-3): n in [1..25]]; // Vincenzo Librandi, Apr 28 2012

<a href="/index/Rec#order_03">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature (7,-3,5).

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A connected (0,1) matrix is one where you can get from any black square, i.e. a 1, , a1, to any other by chess king moves. A matrix is connectable if it is not connected, has rightmost column [1,0,1]' and becomes connected when any of [1,1,1]', [1,1,0]', [0,1,1]' or [0,1,0]' is appended.

_Vincenzo Librandi_, , <a href="/A054420/b054420.txt">Table of n, a(n) for n = 1..1000</a>

<a href="/Sindx_Rea.htmlindex/Rec#recLCCorder_03">Index to sequences with linear recurrences with constant coefficients</a>, signature (7,-3,5).

a(n) = 7*a(n-1) - 3*a(n-2) + 5*a(n-3).

G.f.: x*(1+x)*(1-5*x)/(1 - 7*x + 3*x^2 - 5*x^3). [- _Colin Barker, _, Mar 08 2012]

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_Vincenzo Librandi, _, <a href="/A054420/b054420.txt">Table of n, a(n) for n = 1..1000</a>

a(n) = 7a7*a(n-1)-3a3*a(n-2)+5a5*a(n-3).

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<a href="/Sindx_Rea.html#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (7,-3,5).

<a href="/Sindx_Rea.html#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (7,-3,5).

<a href="/Sindx_Rea.html#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (7,-3,5).

Vincenzo Librandi, <a href="/A054420/b054420.txt">Table of n, a(n) for n = 1..1000</a>

CoefficientList[Series[(1+x)*(1-5*x)/(1-7*x+3*x^2-5*x^3), {x, 0, 30}], x] (* Vincenzo Librandi, Apr 28 2012 *)

(MAGMA) I:=[1, 3, 13]; [n le 3 select I[n] else 7*Self(n-1)-3*Self(n-2)+5*Self(n-3): n in [1..25]]; // Vincenzo Librandi, Apr 28 2012

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More terms from _James A. Sellers (sellersj(AT)math.psu.edu), _, May 23 2000