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A233035
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a(n) = n * floor(n/4).
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4
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0, 0, 0, 4, 5, 6, 7, 16, 18, 20, 22, 36, 39, 42, 45, 64, 68, 72, 76, 100, 105, 110, 115, 144, 150, 156, 162, 196, 203, 210, 217, 256, 264, 272, 280, 324, 333, 342, 351, 400, 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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,4
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COMMENTS
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The maximum number of I patterns tetrominos that can be packed into an n X n array of squares with rotation is prohibited.
u(n) = n*(n mod 4), where u(n) is total number of squares left after packing I patterns into n X n squares.
a(n) = A132028(n) for 4 <= n <= 31.
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LINKS
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Table of n, a(n) for n=1..65.
Kival Ngaokrajang, Illustration of initial terms
Wikipedia, Tetromino
Index entries for linear recurrences with constant coefficients, signature (1,0,0,2,-2,0,0,-1,1).
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FORMULA
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a(n) = (n^2 - n*(n mod 4))/4.
G.f.: (x^7 + x^6 + x^5 + x^4 + 4*x^3)/((1-x)*(1-x^4)^2). - Ralf Stephan, Dec 08 2013
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MATHEMATICA
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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 *)
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PROG
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(Small Basic)
For n = 1 To 100
a = (n*n - n*math.Remainder(n, 4))/4
TextWindow.Write(a+", ")
EndFor
(PARI) a(n) = n * floor(n/4); \\ Joerg Arndt, Dec 08 2013
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CROSSREFS
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Cf. A132028, A233036, A242669.
Sequence in context: A327101 A327082 A154787 * A250036 A107759 A161627
Adjacent sequences: A233032 A233033 A233034 * A233036 A233037 A233038
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KEYWORD
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nonn,easy
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AUTHOR
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Kival Ngaokrajang, Dec 03 2013
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STATUS
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approved
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