A072739 -id:A072739 - cp's OEIS frontend

A072786 Differences between A072782 and A072739.

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

Offset: 0

Antti Karttunen, Jun 12 2002

(define (A072786 n) (- (A072782 n) (A072739 n)))

A072733 Simple triangle-stretching N X N -> N bijection: Inverse of A072732.

Original entry on oeis.org

0, 1, 5, 6, 2, 14, 15, 3, 9, 27, 28, 10, 4, 20, 44, 45, 21, 7, 13, 35, 65, 66, 36, 16, 8, 26, 54, 90, 91, 55, 29, 11, 19, 43, 77, 119, 120, 78, 46, 22, 12, 34, 64, 104, 152, 153, 105, 67, 37, 17, 25, 53, 89, 135, 189, 190, 136, 92, 56, 30, 18, 42, 76, 118, 170, 230, 231

Offset: 0

Antti Karttunen, Jun 12 2002

Index entries for sequences that are permutations of the natural numbers

Inverse: A072732, projections: A072738 & A072739, variant of the same theme: A072735. Cf. also A001477 and its projections A025581 & A002262.

(define (A072733 n) (packA072733 (A025581 n) (A002262 n)))
(define (packA001477 x y) (/ (+ (expt (+ x y) 2) x (* 3 y)) 2))
(define (packA072733 x y) (cond ((<= x y) (let ((half-x (floor->exact (/ x 2)))) (packA001477 half-x (+ half-x (* 2 (- y (* 2 half-x) (modulo x 2))) (modulo x 2))))) (else (let ((half-y (floor->exact (/ y 2)))) (packA001477 (+ 1 half-y (* 2 (- (-1+ x) (* 2 half-y) (modulo y 2))) (modulo y 2)) half-y)))))

A072738 X-projection of the tabular N X N -> N bijection A072733.

Original entry on oeis.org

0, 1, 1, 2, 2, 0, 2, 3, 3, 1, 3, 4, 4, 2, 0, 3, 4, 5, 5, 3, 1, 4, 5, 6, 6, 4, 2, 0, 4, 5, 6, 7, 7, 5, 3, 1, 5, 6, 7, 8, 8, 6, 4, 2, 0, 5, 6, 7, 8, 9, 9, 7, 5, 3, 1, 6, 7, 8, 9, 10, 10, 8, 6, 4, 2, 0, 6, 7, 8, 9, 10, 11, 11, 9, 7, 5, 3, 1, 7, 8, 9, 10, 11, 12, 12, 10, 8, 6, 4, 2, 0, 7, 8, 9, 10, 11, 12, 13

Offset: 0

Antti Karttunen, Jun 12 2002

The Y-projection is A072739. Composition of A025581 & A072732. A072785(n) = A072781(n)-A072738(n).

(define (A072738 n) (A025581 (A072732 n)))

A072782 Y-projection of the tabular N X N -> N bijection A072735.

Original entry on oeis.org

0, 0, 1, 0, 2, 1, 1, 2, 3, 2, 0, 2, 4, 3, 2, 1, 3, 4, 5, 4, 3, 0, 2, 4, 6, 5, 4, 3, 1, 3, 5, 6, 7, 6, 5, 4, 0, 2, 4, 6, 8, 7, 6, 5, 4, 1, 3, 5, 7, 8, 9, 8, 7, 6, 5, 0, 2, 4, 6, 8, 10, 9, 8, 7, 6, 5, 1, 3, 5, 7, 9, 10, 11, 10, 9, 8, 7, 6, 0, 2, 4, 6, 8, 10, 12, 11, 10, 9, 8, 7, 6, 1, 3, 5, 7, 9, 11, 12, 13

Offset: 0

Antti Karttunen, Jun 12 2002

The X-projection is A072781. Composition of A002262 and A072734. A072786(n) = A072782(n)-A072739(n).

(define (A072782 n) (A002262 (A072734 n)))

cp's OEIS Frontend

A072786 Differences between A072782 and A072739.

Views

Author

Keywords

Programs

Scheme

A072733 Simple triangle-stretching N X N -> N bijection: Inverse of A072732.

Views

Author

Keywords

Links

Crossrefs

Programs

Scheme

A072738 X-projection of the tabular N X N -> N bijection A072733.

Views

Author

Keywords

Crossrefs

Programs

Scheme

A072782 Y-projection of the tabular N X N -> N bijection A072735.

Views

Author

Keywords

Crossrefs

Programs

Scheme