|
%I #9 Jan 02 2023 16:49:28
%S 16,34,34,58,68,58,88,112,112,88,124,166,180,166,124,166,230,262,262,
%T 230,166,214,304,358,376,358,304,214,268,388,468,508,508,468,388,268,
%U 328,482,592,658,680,658,592,482,328,394,586,730,826,874,874,826,730,586,394
%N Array read by antidiagonals: T(m,n) = number of spotlight tilings of a width 1 m X n frame.
%H Andrew Howroyd, <a href="/A132370/b132370.txt">Table of n, a(n) for n = 3..1277</a> (first 50 antidiagonals)
%H B. E. Tenner, <a href="http://dx.doi.org/10.1007/s00026-011-0077-6">Spotlight tiling</a>, Ann. Combin. 14 (4) (2010) 553; <a href="https://arxiv.org/abs/0711.1819">arXiv preprint</a>, arXiv:0711.1819 [math.CO], 2007-2008.
%F T(m,n) = 2*(m-2)*(n-2)*(m+n-2) + (m-2)*(m+1) + (n-2)*(n+1).
%e A 3 X 3 frame with width 1 has 16 spotlight tilings.
%e Array begins:
%e ===============================================
%e m/n | 3 4 5 6 7 8 9 10 ...
%e -----+-----------------------------------------
%e 3 | 16 34 58 88 124 166 214 268 ...
%e 4 | 34 68 112 166 230 304 388 482 ...
%e 5 | 58 112 180 262 358 468 592 730 ...
%e 6 | 88 166 262 376 508 658 826 1012 ...
%e 7 | 124 230 358 508 680 874 1090 1328 ...
%e 8 | 166 304 468 658 874 1116 1384 1678 ...
%e 9 | 214 388 592 826 1090 1384 1708 2062 ...
%e 10 | 268 482 730 1012 1328 1678 2062 2480 ...
%e ...
%o (PARI) T(m,n) = 2*(m-2)*(n-2)*(m+n-2) + (m-2)*(m+1) + (n-2)*(n+1) \\ _Andrew Howroyd_, Jan 02 2023
%Y Cf. A051597, A051601.
%K nonn,tabl
%O 3,1
%A _Bridget Tenner_, Nov 09 2007
%E Terms a(31) and beyond from _Andrew Howroyd_, Jan 02 2023
|
