%I M3266 #24 Sep 08 2022 08:44:34
%S 1,4,6,7,7,12,12,19,21,26,26,35,35,46,48,57,57,70,70,85,87,100,100,
%T 117,117,136,138,155,155,176,176,199,201,222,222,247,247,274,276,301,
%U 301,330,330,361,363,392,392,425,425,460,462,495,495,532
%N Number of pair-coverings with largest block size 3.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D R. G. Stanton, J. L. Allston and D. D. Cowan, Pair-coverings with restricted largest block length, Ars Combin., 11 (1981), 85-98.
%D M. J. Grannell, T. S. Griggs, K. A. S. Quinn, R. G. Stanton, A census of minimum pair-coverings with restricted largest block length, Ars Combin., 52 (1999).
%H Vincenzo Librandi, <a href="/A006185/b006185.txt">Table of n, a(n) for n = 3..5000</a>
%H R. G. Stanton, J. L. Allston and D. D. Cowan, <a href="/A006185/a006185.pdf">Pair-coverings with restricted largest block length</a>, Ars Combin., 11 (1981), 85-98. (Annotated scanned copy)
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1,0,0,1,-1,-1,1)
%F a(n) = n*(n-1)/6 if n == 1 or 3 (mod 6), a(n) = n*(n+1)/6 if n == 0 or 2 (mod 6), a(n) = (n^2+n+4)/6 if n == 4 (mod 6), and a(n) = (n^2-n+16)/6 if n == 5 (mod 6). [From Grannell et al.] - _Sean A. Irvine_, Jan 17 2017
%F G.f.: -x^3*(1 + 3*x + x^2 - 2*x^3 + 4*x^5 - x^7 - 2*x^4 - x^6 + x^8) / ( (x^2-x+1)*(1+x+x^2)*(1+x)^2*(x-1)^3 ). - _R. J. Mathar_, Jan 26 2017
%t LinearRecurrence[{1, 1, -1, 0, 0, 1, -1, -1, 1}, {1, 4, 6, 7, 7, 12, 12, 19, 21}, 100] (* _Vincenzo Librandi_, Jan 27 2017 *)
%o (Magma) I:=[1,4,6,7,7,12,12,19,21]; [n le 9 select I[n] else Self(n-1)+Self(n-2)-Self(n-3)+Self(n-6)-Self(n-7)-Self(n-8)+Self(n-9): n in [1..60]]; // _Vincenzo Librandi_, Jan 27 2017
%K nonn,easy
%O 3,2
%A _N. J. A. Sloane_