A288424 -id:A288424 - cp's OEIS frontend

A286294 Leading column of right triangle in A274650.

0, 1, 3, 2, 5, 4, 6, 8, 7, 11, 9, 10, 12, 13, 15, 14, 16, 18, 17, 19, 20, 22, 21, 23, 25, 24, 27, 26, 28, 29, 31, 30, 32, 33, 35, 34, 36, 38, 37, 40, 39, 41, 44, 42, 43, 45, 46, 47, 49, 48, 50, 51, 53, 52, 54, 55, 57, 56, 58, 60, 59, 62, 61, 64, 65, 63, 66, 68, 67, 70, 71, 69, 72, 73, 75, 74, 76, 77, 78

Offset: 0

N. J. A. Sloane, May 30 2017

nonn

Theorem: This is a permutation of the positive integers. For proof, see link in A274650. - N. J. A. Sloane, Jun 07 2017

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Cf. A274650, A274651, A286295, A288384, A288424.

(* function a274651[] is defined in A274651 for n>=1 *)
a286294[n_] := Map[First, a274651[n+1]-1]
a286294[78] (* data *) (* Hartmut F. W. Hoft, Jun 13 2017 *)

a(n) = A274650(n,0) = A274651(n+1,1) - 1. - Hartmut F. W. Hoft, Jun 13 2017

A288384 a(n) is the n-th term of the leading column of the right triangle in A274650 minus n.

Original entry on oeis.org

0, 0, 1, -1, 1, -1, 0, 1, -1, 2, -1, -1, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, -1, 0, 1, -1, 1, -1, 0, 0, 1, -1, 0, 0, 1, -1, 0, 1, -1, 1, -1, 0, 2, -1, -1, 0, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, 1, -1, 0, 1, -1, 1, -1, 1, 1, -2, 0, 1, -1, 1, 1, -2, 0, 0, 1, -1, 0, 0, 0, 1, -1, 2, 0, -2, 0, 0, 1, -1, 1, -1, 0, 1, -1, 1, -1, 0, 0, 1, -1, 0, 0, 1, -1, 0, 1

Offset: 0

Omar E. Pol, Jun 08 2017

sign

It appears that this sequence has infinitely many negative terms, infinitely many zeros and infinitely many positive terms.

Inspired by A286294.
Partial sums give A288424.
Cf. A274650, A274651.

(* function a286294[] is defined in A286294 using A274651 *)
a288384[n_] := a286294[n] - Range[0,n]
a288384[104] (* data *) (* Hartmut F. W. Hoft, Jun 13 2017 *)

a(n) = A274650(n,0) - n = A286294(n) - n, n >= 0.

Signs reversed at the suggestion of Hartmut F. W. Hoft and edited by Omar E. Pol, Jun 13 2017

cp's OEIS Frontend

A286294 Leading column of right triangle in A274650.

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