A079326 a(n) = the largest number m such that if m monominoes are removed from an n X n square then an L-tromino must remain.

1, 2, 7, 9, 17, 20, 31, 35, 49, 54, 71, 77, 97, 104, 127, 135, 161, 170, 199, 209, 241, 252, 287, 299, 337, 350, 391, 405, 449, 464, 511, 527, 577, 594, 647, 665, 721, 740, 799, 819, 881, 902, 967, 989, 1057, 1080, 1151, 1175, 1249, 1274, 1351, 1377, 1457

Offset: 2

Author

Mambetov Timur (timur_teufel(AT)mail.ru), Feb 13 2003

Keywords

• nonn
• easy

Examples

			a(3)=2 because if a middle row of 3 monominoes are removed from the 3 X 3, no L remains.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Crossrefs

Frobenius number for k successive numbers: A028387 (k=2), this sequence (k=3), A138984 (k=4), A138985 (k=5), A138986 (k=6), A138987 (k=7), A138988 (k=8).

Cf. A093353, A104519.

Programs

Mathematica

Table[FrobeniusNumber[{a, a + 1, a + 2}], {a, 2, 54}] (* Zak Seidov, Jan 08 2015 *)

Formula

a(n) = (n^2)/2 - 1 (n even), (n^2-n)/2 - 1 (n odd).

a(n) = A204557(n-1) / (n-1). - Reinhard Zumkeller, Jan 18 2012

From Bruno Berselli, Jan 18 2011: (Start)

G.f.: x^2*(1+x+3*x^2-x^4)/((1+x)^2*(1-x)^3).

a(n) = n*(2*n+(-1)^n-1)/4 - 1.

a(n) = A105638(-n+2). (End)

Extensions

Edited by Don Reble, May 28 2007