A217764 - OEIS

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

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OFFSET

0,2

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.

LINKS

Table of n, a(n) for n=0..65.

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.

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.

EXAMPLE

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.

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).

Sequence in context: A254006 A321329 A016645 * A096429 A196622 A196827

Adjacent sequences: A217761 A217762 A217763 * A217765 A217766 A217767

KEYWORD

nonn,tabl

AUTHOR

Ross La Haye, Mar 23 2013

STATUS

approved