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

1,4

COMMENTS

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.

LINKS

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).

FORMULA

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

PROG

(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

CROSSREFS

Cf. A132028, A233036, A242669.

Sequence in context: A327101 A327082 A154787 * A250036 A107759 A161627

Adjacent sequences:  A233032 A233033 A233034 * A233036 A233037 A233038

KEYWORD

nonn,easy

AUTHOR

Kival Ngaokrajang, Dec 03 2013

STATUS

approved

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Last modified February 27 10:15 EST 2020. Contains 332304 sequences. (Running on oeis4.)