A286559 Compound filter (the left & right summand of Hofstadter Q-sequence): a(n) = P(Q(n-Q(n-1)), Q(n-Q(n-2))), where P(n,k) is sequence A000027 used as a pairing function, with a(1) = a(2) = 0.

0, 0, 1, 2, 2, 5, 8, 8, 13, 13, 13, 25, 24, 25, 41, 32, 41, 50, 50, 61, 61, 61, 61, 113, 84, 86, 113, 113, 113, 113, 181, 128, 129, 181, 200, 163, 182, 221, 200, 221, 242, 242, 265, 265, 265, 265, 265, 481, 263, 290, 420, 363, 314, 422, 420, 365, 481, 420, 481, 481, 481, 481, 761, 512, 452, 687, 577, 513, 722, 761, 650, 687, 762, 723, 760, 722, 842, 760, 801

Offset: 1

Author

Antti Karttunen, May 18 2017

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..67390
• Eric Weisstein's World of Mathematics, Pairing Function

Crossrefs

Cf. A005185, A283467, A286541, A286560.

Programs

Scheme

(define (A286559 n) (if (<= n 2) 0 (* (/ 1 2) (+ (expt (+ (A005185 (- n (A005185 (- n 1)))) (A005185 (- n (A005185 (- n 2))))) 2) (- (A005185 (- n (A005185 (- n 1))))) (- (* 3 (A005185 (- n (A005185 (- n 2)))))) 2))))

Formula

a(1) = a(2) = 0, for n > 2, a(n) = (1/2)*(2 + ((A005185(n-A005185(n-1))+A005185(n-A005185(n-2)))^2) - A005185(n-A005185(n-1)) - 3*A005185(n-A005185(n-2))).