A072741 -id:A072741 - cp's OEIS frontend

A072784 Differences between A072741 and A072737.

0, 0, -1, 0, 1, -1, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, -1, 1, -1, 0, 0, 0, 1, -1, 1, -1, 0, 0, 0, 0, 1, -1, 1, -1, 0, 0, 0, 0, 0, 1, -1, 1, -1, 0, 0, 0, 0, 0, -1, 1, -1, 1, -1, 0, 0, 0, 0, 0, 1, -1, 1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 1, -1, 1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1

Offset: 0

Antti Karttunen, Jun 12 2002

(define (A072784 n) (- (A072741 n) (A072737 n)))

A072734 Simple triangle-stretching N X N -> N bijection, variant of A072732.

Original entry on oeis.org

0, 1, 2, 3, 12, 4, 7, 17, 18, 5, 6, 23, 40, 24, 8, 11, 31, 49, 50, 25, 9, 10, 30, 59, 84, 60, 32, 13, 16, 39, 71, 97, 98, 61, 33, 14, 15, 38, 70, 111, 144, 112, 72, 41, 19, 22, 48, 83, 127, 161, 162, 113, 73, 42, 20, 21, 47, 82, 126, 179, 220, 180, 128, 85, 51, 26, 29, 58

Offset: 0

Antti Karttunen, Jun 12 2002

Index entries for sequences that are permutations of the natural numbers

Inverse: A072735, projections: A072740 & A072741, variant of the same theme: A072732. Used to construct the global arithmetic ranking scheme of plane binary trees presented in A072787/A072788. Cf. also A001477 and its projections A025581 & A002262.

(define (A072734 n) (packA072734 (A025581 n) (A002262 n)))
(define (packA001477 x y) (/ (+ (expt (+ x y) 2) x (* 3 y)) 2))
(define (packA072734 x y) (let ((x-y (- x y))) (cond ((negative? x-y) (packA001477 (+ (* 2 x) (modulo (1+ x-y) 2)) (+ (* 2 x) (floor->exact (/ (+ (- x-y) (modulo x-y 2)) 2))))) ((< x-y 3) (packA001477 (+ (* 2 y) x-y) (* 2 y))) (else (packA001477 (+ (* 2 y) (floor->exact (/ (1+ x-y) 2)) (modulo (1+ x-y) 2)) (+ (* 2 y) (modulo x-y 2)))))))

A072740 X-projection of the tabular N X N -> N bijection A072734.

Original entry on oeis.org

0, 1, 0, 2, 0, 0, 4, 3, 0, 0, 6, 5, 1, 0, 0, 8, 7, 2, 1, 0, 0, 10, 9, 3, 1, 1, 0, 0, 12, 11, 5, 4, 1, 1, 0, 0, 14, 13, 7, 6, 2, 1, 1, 0, 0, 16, 15, 9, 8, 3, 2, 1, 1, 0, 0, 18, 17, 11, 10, 4, 2, 2, 1, 1, 0, 0, 20, 19, 13, 12, 6, 5, 2, 2, 1, 1, 0, 0, 22, 21, 15, 14, 8, 7, 3, 2, 2, 1, 1, 0, 0, 24, 23

Offset: 0

Antti Karttunen, Jun 12 2002

The Y-projection is A072741. Composition of A025581 and A072735. A072783(n) = A072740(n)-A072736(n).

(define (A072740 n) (A025581 (A072735 n)))

A072737 Y-projection of the tabular N X N -> N bijection A072732.

Original entry on oeis.org

0, 0, 2, 0, 1, 4, 0, 0, 3, 6, 0, 0, 1, 5, 8, 0, 0, 1, 3, 7, 10, 0, 0, 1, 2, 5, 9, 12, 0, 0, 1, 1, 4, 7, 11, 14, 0, 0, 1, 1, 2, 6, 9, 13, 16, 0, 0, 1, 1, 2, 4, 8, 11, 15, 18, 0, 0, 1, 1, 2, 3, 6, 10, 13, 17, 20, 0, 0, 1, 1, 2, 2, 5, 8, 12, 15, 19, 22, 0, 0, 1, 1, 2, 2, 3, 7, 10, 14, 17, 21, 24, 0, 0

Offset: 0

Antti Karttunen, Jun 12 2002

The X-projection is A072736. Composition of A002262 and A072733. A072784(n) = A072741(n)-A072737(n).

(define (A072737 n) (A002262 (A072733 n)))

A072788 Inverse permutation to A072787.

Original entry on oeis.org

0, 1, 3, 2, 8, 5, 4, 22, 7, 13, 10, 17, 18, 6, 9, 36, 21, 64, 19, 15, 12, 27, 46, 50, 16, 14, 41, 24, 31, 59, 58, 47, 60, 38, 37, 32, 11, 45, 20, 191, 44, 52, 120, 40, 23, 78, 63, 148, 144, 56, 43, 51, 111, 108, 35, 106, 61, 196, 168, 131, 178, 153, 150, 115, 116, 33, 29

Offset: 0

Antti Karttunen, Jun 12 2002

A. Karttunen, Gatomorphisms
Index entries for sequences that are permutations of the natural numbers

Inverse permutation: A072787. Cf. also A072740, A072741, A072789.

cp's OEIS Frontend

A072784 Differences between A072741 and A072737.

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A072734 Simple triangle-stretching N X N -> N bijection, variant of A072732.

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A072740 X-projection of the tabular N X N -> N bijection A072734.

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A072737 Y-projection of the tabular N X N -> N bijection A072732.

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A072788 Inverse permutation to A072787.

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