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%I #29 Aug 22 2020 15:32:12
%S 0,0,0,4,5,6,7,16,18,20,22,36,39,42,45,64,68,72,76,100,105,110,115,
%T 144,150,156,162,196,203,210,217,256,264,272,280,324,333,342,351,400,
%U 410,420,430,484,495,506,517,576,588,600,612,676,689,702,715,784,798,812,826,900,915,930,945,1024,1040
%N a(n) = n * floor(n/4).
%C The maximum number of I patterns tetrominos that can be packed into an n X n array of squares with rotation is prohibited.
%C u(n) = n*(n mod 4), where u(n) is total number of squares left after packing I patterns into n X n squares.
%C a(n) = A132028(n) for 4 <= n <= 31.
%H Kival Ngaokrajang, <a href="/A233035/a233035.pdf">Illustration of initial terms</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Tetromino">Tetromino</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,2,-2,0,0,-1,1).
%F a(n) = (n^2 - n*(n mod 4))/4.
%F G.f.: (x^7 + x^6 + x^5 + x^4 + 4*x^3)/((1-x)*(1-x^4)^2). - _Ralf Stephan_, Dec 08 2013
%t Table[n*Floor[n/4],{n,80}] (* or *) LinearRecurrence[{1,0,0,2,-2,0,0,-1,1},{0,0,0,4,5,6,7,16,18},80] (* _Harvey P. Dale_, Aug 22 2020 *)
%o (Small Basic)
%o For n = 1 To 100
%o a = (n*n - n*math.Remainder(n,4))/4
%o TextWindow.Write(a+", ")
%o EndFor
%o (PARI) a(n) = n * floor(n/4); \\ _Joerg Arndt_, Dec 08 2013
%Y Cf. A132028, A233036, A242669.
%K nonn,easy
%O 1,4
%A _Kival Ngaokrajang_, Dec 03 2013
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