A072733 -id:A072733 - cp's OEIS frontend

A072735 Simple triangle-stretching N X N -> N bijection: Inverse of A072734, variant of A072733.

0, 1, 2, 3, 5, 9, 10, 6, 14, 20, 21, 15, 4, 27, 35, 36, 28, 7, 8, 44, 54, 55, 45, 11, 13, 19, 65, 77, 78, 66, 22, 16, 26, 34, 90, 104, 105, 91, 37, 29, 12, 43, 53, 119, 135, 136, 120, 56, 46, 17, 18, 64, 76, 152, 170, 171, 153, 79, 67, 23, 25, 33, 89, 103, 189, 209, 210

Offset: 0

Antti Karttunen, Jun 12 2002

Index entries for sequences that are permutations of the natural numbers

Inverse: A072734, projections: A072781 & A072782, variant of the same theme: A072733. Cf. also A001477 and its projections A025581 & A002262.

(define (A072735 n) (packA072735 (A025581 n) (A002262 n)))
(define (packA001477 x y) (/ (+ (expt (+ x y) 2) x (* 3 y)) 2))
(define (packA072735 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) (if (and (eq? x y) (even? x)) 0 -1))))) (else (let ((half-y (floor->exact (/ y 2)))) (packA001477 (+ half-y (* 2 (- (-1+ x) (* 2 half-y))) (modulo y 2) (if (and (eq? x (1+ y)) (even? y)) 1 0)) 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)))

A072739 Y-projection of the tabular N X N -> N bijection A072733.

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, Jun 12 2002

The X-projection is A072738. Composition of A002262 and A072732. A072786(n) = A072782(n)-A072739(n).

(define (A072739 n) (A002262 (A072732 n)))

A072732 Simple triangle-stretching N X N -> N bijection: push terms in the middle twice as far down to make space for the terms obtained by bisecting the edges, which are thus contracted by the same factor. Do this for all "triangle-shells" successively contained inside each other in A001477.

Original entry on oeis.org

0, 1, 4, 7, 12, 2, 3, 17, 24, 8, 11, 31, 40, 18, 5, 6, 23, 49, 60, 32, 13, 16, 39, 71, 84, 50, 25, 9, 10, 30, 59, 97, 112, 72, 41, 19, 22, 48, 83, 127, 144, 98, 61, 33, 14, 15, 38, 70, 111, 161, 180, 128, 85, 51, 26, 29, 58, 96, 143, 199, 220, 162, 113, 73, 42, 20, 21, 47

Offset: 0

Antti Karttunen, Jun 12 2002

Index entries for sequences that are permutations of the natural numbers

Inverse: A072733, projections: A072736 & A072737, variant of the same theme: A072734. Cf. also A001477 and its projections A025581 & A002262.

(define (A072732 n) (packA072732 (A025581 n) (A002262 n)))
(define (packA001477 x y) (/ (+ (expt (+ x y) 2) x (* 3 y)) 2))
(define (packA072732 x y) (let ((x-y (- x y))) (cond ((<= x-y 0) (packA001477 (+ (* 2 x) (modulo x-y 2)) (+ (* 2 x) (floor->exact (/ (1+ (- x-y)) 2))))) (else (packA001477 (+ (* 2 (1+ y)) (floor->exact (/ (- x-y 2) 2))) (+ (* 2 y) (modulo (1+ x-y) 2)))))))

A072736 X-projection of the tabular N X N -> N bijection A072732.

Original entry on oeis.org

0, 1, 0, 3, 0, 0, 5, 2, 0, 0, 7, 4, 1, 0, 0, 9, 6, 2, 1, 0, 0, 11, 8, 4, 1, 1, 0, 0, 13, 10, 6, 3, 1, 1, 0, 0, 15, 12, 8, 5, 2, 1, 1, 0, 0, 17, 14, 10, 7, 3, 2, 1, 1, 0, 0, 19, 16, 12, 9, 5, 2, 2, 1, 1, 0, 0, 21, 18, 14, 11, 7, 4, 2, 2, 1, 1, 0, 0, 23, 20, 16, 13, 9, 6, 3, 2, 2, 1, 1, 0, 0, 25, 22

Offset: 0

Antti Karttunen, Jun 12 2002

The Y-projection is A072737. Composition of A025581 & A072733. A072783(n) = A072740(n)-A072736(n).

(define (A072736 n) (A025581 (A072733 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)))

cp's OEIS Frontend

A072735 Simple triangle-stretching N X N -> N bijection: Inverse of A072734, variant of A072733.

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

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A072739 Y-projection of the tabular N X N -> N bijection A072733.

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A072732 Simple triangle-stretching N X N -> N bijection: push terms in the middle twice as far down to make space for the terms obtained by bisecting the edges, which are thus contracted by the same factor. Do this for all "triangle-shells" successively contained inside each other in A001477.

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A072736 X-projection of the tabular N X N -> N bijection A072732.

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

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