cp's OEIS Frontend

A179618 T(n,k) = Half the number of (n+1) X (k+1) 0..2 arrays with every 2 X 2 subblock diagonal sum differing from its antidiagonal sum by more than 2.

%I A179618 #22 Jan 01 2023 09:47:00
%S A179618 5,11,11,21,35,21,43,93,93,43,85,269,314,269,85,171,747,1213,1213,747,
%T A179618 171,341,2115,4375,6427,4375,2115,341,683,5933,16334,31387,31387,
%U A179618 16334,5933,683,1365,16717,59925,159651,202841,159651,59925,16717,1365,2731
%N A179618 T(n,k) = Half the number of (n+1) X (k+1) 0..2 arrays with every 2 X 2 subblock diagonal sum differing from its antidiagonal sum by more than 2.
%C A179618 T(n,k) apparently is also the number of ways to tile an (n+2) X (k+2) rectangle with 1 X 1 and 2 X 2 tiles.
%H A179618 R. H. Hardin, <a href="/A179618/b179618.txt">Table of n, a(n) for n = 1..839</a>
%e A179618 Table starts
%e A179618      5     11      21        43         85         171           341
%e A179618     11     35      93       269        747        2115          5933
%e A179618     21     93     314      1213       4375       16334         59925
%e A179618     43    269    1213      6427      31387      159651        795611
%e A179618     85    747    4375     31387     202841     1382259       9167119
%e A179618    171   2115   16334    159651    1382259    12727570     113555791
%e A179618    341   5933   59925    795611    9167119   113555791    1355115601
%e A179618    683  16717  221799   4005785   61643709  1029574631   16484061769
%e A179618   1365  47003  817280  20064827  411595537  9258357134  198549329897
%e A179618   2731 132291 3018301 100764343 2758179839 83605623809 2403674442213
%e A179618 Some solutions for 6 X 6:
%e A179618   0 2 0 2 0 2    0 1 0 2 1 2    0 2 0 2 0 2    0 1 0 2 0 1
%e A179618   2 0 2 0 2 1    2 0 2 0 2 0    2 0 1 0 1 0    2 0 2 0 2 0
%e A179618   0 2 0 2 0 2    1 2 1 2 0 2    0 2 0 2 0 2    0 2 0 2 0 2
%e A179618   2 0 2 0 2 1    2 0 2 0 1 0    1 0 2 0 2 0    1 0 2 0 2 0
%e A179618   0 2 0 2 0 2    0 2 0 2 0 2    0 2 0 2 0 2    0 2 1 2 1 2
%e A179618   1 0 1 0 1 0    2 1 2 1 2 0    2 1 2 1 2 1    2 0 2 0 2 0
%Y A179618 Diagonal is A063443(n+2).
%Y A179618 Column 1 is A001045(n+3).
%Y A179618 Column 2 is A054854(n+2).
%Y A179618 Column 3 is A054855(n+2).
%Y A179618 Column 4 is A063650(n+2).
%Y A179618 Column 5 is A063651(n+2).
%Y A179618 Column 6 is A063652(n+2).
%Y A179618 Column 7 is A063653(n+2).
%Y A179618 Column 8 is A063654(n+2).
%K A179618 nonn,tabl
%O A179618 1,1
%A A179618 _R. H. Hardin_, Jan 10 2011