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

Offset: 1

Author

Kival Ngaokrajang, Dec 03 2013

Keywords

• nonn
• easy

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

• 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).

Crossrefs

Cf. A132028, A233036, A242669.

Programs

Mathematica

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 *)

PARI

a(n) = n * floor(n/4); \\ Joerg Arndt, Dec 08 2013

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