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

3,1

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.

Formula

T(m,n) = 2*(m-2)*(n-2)*(m+n-2) + (m-2)*(m+1) + (n-2)*(n+1).

Example

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 ...
  ...

Prog

(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

Crossrefs

Cf. A051597, A051601.

Sequence in context: A144533 A041510 A070590 * A185467 A245664 A091216

Adjacent sequences: A132367 A132368 A132369 * A132371 A132372 A132373

Keyword

nonn,tabl

Author

Bridget Tenner, Nov 09 2007

Extensions

Terms a(31) and beyond from Andrew Howroyd, Jan 02 2023

Status

approved