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%I #33 Aug 11 2022 03:40:59
%S 1,4,13,34,73,136,229,358,529,748,1021,1354,1753,2224,2773,3406,4129,
%T 4948,5869,6898,8041,9304,10693,12214,13873,15676,17629,19738,22009,
%U 24448,27061,29854,32833,36004,39373,42946,46729,50728,54949
%N Row sums of triangle A135858.
%C Number of binary 3 X (n-1) matrices such that each row and column has at most one 1. - _Dmitry Kamenetsky_, Jan 20 2018
%H Vincenzo Librandi, <a href="/A135859/b135859.txt">Table of n, a(n) for n = 1..1000</a>
%H R. J. Mathar, <a href="/A247158/a247158.pdf">The number of binary matrices...</a>, Table 1 column 3.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F Row sums of triangle A135858. Binomial transform of [1, 3, 6, 6, 0, 0, 0, ...].
%F G.f.: x*(1+3*x^2+2*x^3) / (1-x)^4. - _R. J. Mathar_, Apr 04 2012
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - _Vincenzo Librandi_, Jun 29 2012
%F a(n) = n^3 - 3*n^2 + 5*n - 2. - _R. J. Mathar_, Oct 20 2017
%F E.g.f.: 2 - (2 - 3*x - x^3)*exp(x). - _G. C. Greubel_, Aug 11 2022
%e a(3) = 13 = sum of row 3 terms of triangle A135858: (7, + 5 + 1).
%e a(4) = 34 = (1, 3, 3, 1) dot (1, 3, 6, 6) = (1 + 9 + 18 + 6).
%p seq(5*n - 2 + n^3 - 3*n^2, n=1..10^2); # _Muniru A Asiru_, Jan 24 2018
%t CoefficientList[Series[(1+3*x^2+2*x^3)/(x-1)^4,{x,0,40}],x] (* _Vincenzo Librandi_, Jun 29 2012 *)
%o (Magma) I:=[1, 4, 13, 34]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // _Vincenzo Librandi_, Jun 29 2012
%o (GAP) List([1..10^4], n-> 5*n - 2 + n^3 - 3*n^2); # _Muniru A Asiru_, Jan 24 2018
%o (SageMath) [n^3 -3*n^2 +5*n -2 for n in (1..50)] # _G. C. Greubel_, Aug 11 2022
%Y Cf. A135858.
%K nonn,easy
%O 1,2
%A _Gary W. Adamson_, Dec 01 2007
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