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

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, 3, 1, 2187, 665, 454, 130, 65, 15, 6, 0, 6561, 2059, 1394, 422, 211, 57, 24, 4, 1, 19683, 6305, 4246, 1330, 665, 195, 84, 20, 7, 0, 59049, 19171, 12866, 4118, 2059, 633, 276, 76, 29, 5, 1

Offset: 0

Author

Ross La Haye, Mar 23 2013

Keywords

• nonn
• tabl

Comments

Columns 0,1,2,3 respectively correspond to relations R_3, R_4, R_0, R_1 defined in La Haye paper listed below.

Examples

			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.
		

Links

• Ross La Haye, Binary Relations on the Power Set of an n-Element Set, Journal of Integer Sequences, Vol. 12 (2009), Article 09.2.6.

Crossrefs

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).

Formula

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.