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A217764 Array defined by a(n,k) = floor((k+2)/2)*3^n - floor((k+1)/2)*2^n, read by antidiagonals.

%I A217764 #20 Nov 01 2024 02:01:49
%S A217764 1,3,0,9,1,1,27,5,4,0,81,19,14,2,1,243,65,46,10,5,0,729,211,146,38,19,
%T A217764 3,1,2187,665,454,130,65,15,6,0,6561,2059,1394,422,211,57,24,4,1,
%U A217764 19683,6305,4246,1330,665,195,84,20,7,0,59049,19171,12866,4118,2059,633,276,76,29,5,1
%N A217764 Array defined by a(n,k) = floor((k+2)/2)*3^n - floor((k+1)/2)*2^n, read by antidiagonals.
%C A217764 Columns 0,1,2,3 respectively correspond to relations R_3, R_4, R_0, R_1 defined in La Haye paper listed below.
%H A217764 Ross La Haye, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL12/LaHaye/lahaye5.html">Binary Relations on the Power Set of an n-Element Set</a>, Journal of Integer Sequences, Vol. 12 (2009), Article 09.2.6.
%F A217764 a(n,k) = floor((k+2)/2)*3^n - floor((k+1)/2)*2^n. a(n,k) = 5*a(n-1,k) - 6*a(n-2,k); a(0,k) = floor((k+2)/2) - floor((k+1)/2), a(1,k) = floor((k+2)/2)*3 - floor((k+1)/2)*2.
%e A217764 a(4,4) = 211 because floor((4+2)/2)*3^4 - floor((4+1)/2)*2^4 = 3*3^4 - 2*2^4 = 243 - 32 = 211.
%Y A217764 Cf. a(1,k) = A084964(k+2); a(n,0) = A000244(n); a(n,1) = A001047(n); a(n,2) = A027649(n); a(n,3) = A056182(n); a(n,4) = A001047(n+1); a(n,5) = A210448(n); a(n,6) = A166060(n); a(n,7) = A145563(n); a(n,8) = A102485(n).
%K A217764 nonn,tabl
%O A217764 0,2
%A A217764 _Ross La Haye_, Mar 23 2013