A132370 Array read by antidiagonals: T(m,n) = number of spotlight tilings of a width 1 m X n frame.
16, 34, 34, 58, 68, 58, 88, 112, 112, 88, 124, 166, 180, 166, 124, 166, 230, 262, 262, 230, 166, 214, 304, 358, 376, 358, 304, 214, 268, 388, 468, 508, 508, 468, 388, 268, 328, 482, 592, 658, 680, 658, 592, 482, 328, 394, 586, 730, 826, 874, 874, 826, 730, 586, 394
Offset: 3
Examples
A 3 X 3 frame with width 1 has 16 spotlight tilings. Array begins: =============================================== m/n | 3 4 5 6 7 8 9 10 ... -----+----------------------------------------- 3 | 16 34 58 88 124 166 214 268 ... 4 | 34 68 112 166 230 304 388 482 ... 5 | 58 112 180 262 358 468 592 730 ... 6 | 88 166 262 376 508 658 826 1012 ... 7 | 124 230 358 508 680 874 1090 1328 ... 8 | 166 304 468 658 874 1116 1384 1678 ... 9 | 214 388 592 826 1090 1384 1708 2062 ... 10 | 268 482 730 1012 1328 1678 2062 2480 ... ...
Links
- Andrew Howroyd, Table of n, a(n) for n = 3..1277 (first 50 antidiagonals)
- B. E. Tenner, Spotlight tiling, Ann. Combin. 14 (4) (2010) 553; arXiv preprint, arXiv:0711.1819 [math.CO], 2007-2008.
Programs
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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
Formula
T(m,n) = 2*(m-2)*(n-2)*(m+n-2) + (m-2)*(m+1) + (n-2)*(n+1).
Extensions
Terms a(31) and beyond from Andrew Howroyd, Jan 02 2023