A072736 -id:A072736 - cp's OEIS frontend

A072783 Differences between A072740 and A072736.

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

Offset: 0

Antti Karttunen, Jun 12 2002

(define (A072783 n) (- (A072740 n) (A072736 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)))))))

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)))

cp's OEIS Frontend

A072783 Differences between A072740 and A072736.

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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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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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