A072738 -id:A072738 - cp's OEIS frontend

A072785 Differences between A072781 and A072738.

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

Offset: 0

Antti Karttunen, Jun 12 2002

Boris Putievskiy, Transformations [of] Integer Sequences And Pairing Functions, 2012, arXiv:1212.2732 [math.CO], 2012.

Cf. A130517, A162630.

(define (A072785 n) (- (A072781 n) (A072738 n)))

From Boris Putievskiy, Jan 16 2013: (Start)
a(n) =  floor((2*A000027(n)-A003056(n)^2-A003056(n))/(A003056(n)+3))*(-1)^A003056(n).
a(n) =  floor((2*n-t*t-t)/(t+3))*(-1)^t where t=floor((-1+sqrt(8*n-7))/2).
(End)

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)))))

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)))

A072781 X-projection of the tabular N X N -> N bijection A072735.

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, Jun 12 2002

The Y-projection is A072782. Composition of A025581 & A072734. A072785(n) = A072781(n)-A072738(n).

(define (A072781 n) (A025581 (A072734 n)))

cp's OEIS Frontend

A072785 Differences between A072781 and A072738.

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

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

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A072781 X-projection of the tabular N X N -> N bijection A072735.

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