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

2,2

Links

Table of n, a(n) for n=2..54.

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

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)

Example

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

Mathematica

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

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.

Sequence in context: A042807 A005988 A199537 * A055673 A177737 A336770

Adjacent sequences: A079323 A079324 A079325 * A079327 A079328 A079329

Keyword

nonn,easy

Author

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

Extensions

Edited by Don Reble, May 28 2007

Status

approved