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%I #20 Sep 08 2022 08:44:37
%S 0,0,0,0,0,0,0,1,1,2,2,3,4,5,5,6,7,8,9,11,12,13,14,16,17,19,20,22,24,
%T 26,28,30,32,34,36,38,40,42,45,47,50,52,55,58,61,63,66,69,72,75,79,82,
%U 85,88,92,95,99,102,106,110,114,118,122,126,130,134,138,142,146,151,155,160
%N Floor(n(n - 1)/31).
%H Vincenzo Librandi, <a href="/A011884/b011884.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_33">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1).
%F G.f.: -((x^7 (1+x^5-2 x^7+x^9+x^14) (1+(-1+x) x (1+(-1+x) x) (1+x+x^2)))/(-1+x (2+x (-1+(-1+x)^2 x^29)))). - _Peter J. C. Moses_, Jun 01 2014
%F a(0)=0, a(1)=0, a(2)=0, a(3)=0, a(4)=0, a(5)=0, a(6)=0, a(7)=1, a(8)=1, a(9)=2, a(10)=2, a(11)=3, a(12)=4, a(13)=5, a(14)=5, a(15)=6, a(16)=7, a(17)=8, a(18)=9, a(19)=11, a(20)=12, a(21)=13, a(22)=14, a(23)=16, a(24)=17, a(25)=19, a(26)=20, a(27)=22, a(28)=24, a(29)=26, a(30)=28, a(31)=30, a(32)=32, a(n)=2*a(n-1)-a(n-2)+a(n-31)- 2*a(n-32)+ a(n-33). - _Harvey P. Dale_, Jan 23 2016
%e a(11) = 3 because 11 * 10/31 = 3.548387...
%e a(12) = 4 because 12 * 11/31 = 4.258...
%e a(13) = 5 because 13 * 12/31 = 5.032258...
%p A011884:=n->floor(n*(n-1)/31); seq(A011884(n), n=0..50); # _Wesley Ivan Hurt_, Jun 01 2014
%t Table[Floor[n(n - 1)/31], {n, 0, 79}] (* _Alonso del Arte_, Apr 13 2014 *)
%t CoefficientList[Series[-((x^7 (1 + x^5 - 2 x^7 + x^9 + x^14) (1 + (-1 + x) x (1 + (-1 + x) x) (1 + x + x^2)))/(-1 + x (2 + x (-1 + (-1 + x)^2 x^29)))), {x, 0, 100}], x] (* _Vincenzo Librandi_, Jun 02 2014 *)
%t LinearRecurrence[{2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-2,1},{0,0,0,0,0,0,0,1,1,2,2,3,4,5,5,6,7,8,9,11,12,13,14,16,17,19,20,22,24,26,28,30,32},80] (* _Harvey P. Dale_, Jan 23 2016 *)
%o (Magma) [Floor(n*(n-1)/31): n in [0..50]]; // _Wesley Ivan Hurt_, Jun 01 2014
%K nonn,easy
%O 0,10
%A _N. J. A. Sloane_, Dec 11 1996
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