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%I #44 May 06 2021 08:11:01
%S 0,3,1,4,2,2,6,3,4,3,8,6,6,6,6,14,9,11,10,11,9,20,18,18,18,18,18,18,
%T 36,30,33,30,34,30,33,30,60,56,56,58,56,56,58,56,56,108,99,105,99,105,
%U 100,105,99,105,99,188,186,186,186,186,186,186,186,186,186,186,352,335,344,338,346,335,348,335,346,338,344,335,632,630,630,630,630,630,630,630,630,630,630,630,630,1182,1161,1179,1161,1179,1161,1179,1162,1179,1161,1179,1161,1179,1161,2192,2182,2182,2188,2182,2184,2188,2182,2182,2188,2184,2182,2188,2182,2182
%N Triangle read by rows: T(n,k), 0 <= k <= n-1, = number of 2-divided binary sequences of length n which are 2-divisible in exactly k ways.
%C Computed by _David Scambler_.
%C See A210109 for further information.
%C Omitting the leading column, triangle has mirror symmetry.
%C Speculation: T(2n+1,2)=T(2n+1,1); T(2n,2)=T(2n,1)+T(n,1); T(3n+1,3)=T(3n+1,1); T(3n+2,3)=T(3n+2,1); T(3n,3)=T(3n,1)+T(n,1) and similar "lagged modulo sums" for T(4n+i,4)=T(4n+i,2), 0<i<=3; T(4n,4)=T(4n,2)+T(n,1); T(5n+i,5)=T(5n+i,1), 0<i<=4; T(5n,5)=T(5n,1)+T(n,1). - _R. J. Mathar_, Mar 27 2012
%C Right border appears to be A059966. - _Michel Marcus_, Apr 26 2013
%e Triangle begins:
%e n k=0 k=1 k=2 k=3 k=4 k=5 k=6 k=7 k=8 k=9 k=10 k=11 k=12 k=13 k=14
%e 1 1
%e 2 3 1
%e 3 4 2 2
%e 4 6 3 4 3
%e 5 8 6 6 6 6
%e 6 14 9 11 10 11 9
%e 7 20 18 18 18 18 18 18
%e 8 36 30 33 30 34 30 33 30
%e 9 60 56 56 58 56 56 58 56 56
%e 10 108 99 105 99 105 100 105 99 105 99
%e 11 188 186 186 186 186 186 186 186 186 186 186
%e 12 352 335 344 338 346 335 348 335 346 338 344 335
%e 13 632 630 630 630 630 630 630 630 630 630 630 630 630
%e 14 1182 1161 1179 1161 1179 1161 1179 1162 1179 1161 1179 1161 1179 1161
%e 15 2192 2182 2182 2188 2182 2184 2188 2182 2182 2188 2184 2182 2188 2182 2182...
%Y First column is A000031, second column is conjectured to be A001037. Row sums = 2^n.
%K nonn,tabl
%O 1,2
%A _N. J. A. Sloane_, Mar 21 2012
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