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A233035 a(n) = n * floor(n/4). 4

%I

%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

%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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Last modified April 9 20:46 EDT 2020. Contains 333363 sequences. (Running on oeis4.)