A072737 -id:A072737 - 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)))

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)))))))

A072741 Y-projection of the tabular N X N -> N bijection A072734.

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, Jun 12 2002

The X-projection is A072740. Composition of A002262 & A072735. A072784(n) = A072741(n)-A072737(n).

(define (A072741 n) (A002262 (A072735 n)))

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)))

cp's OEIS Frontend

A072784 Differences between A072741 and A072737.

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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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A072741 Y-projection of the tabular N X N -> N bijection A072734.

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

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