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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.
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%I #22 Jan 28 2023 22:08:47

%S 1,2,7,9,17,20,31,35,49,54,71,77,97,104,127,135,161,170,199,209,241,

%T 252,287,299,337,350,391,405,449,464,511,527,577,594,647,665,721,740,

%U 799,819,881,902,967,989,1057,1080,1151,1175,1249,1274,1351,1377,1457

%N 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.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).

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

%F a(n) = A204557(n-1) / (n-1). - _Reinhard Zumkeller_, Jan 18 2012

%F From _Bruno Berselli_, Jan 18 2011: (Start)

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

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

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

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

%t Table[FrobeniusNumber[{a, a + 1, a + 2}], {a, 2, 54}] (* _Zak Seidov_, Jan 08 2015 *)

%Y 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).

%Y Cf. A093353, A104519.

%K nonn,easy

%O 2,2

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

%E Edited by _Don Reble_, May 28 2007