A318958 - OEIS

A318958

A(n, k) is a square array read in the decreasing antidiagonals, for n >= 0 and k >= 0.

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

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OFFSET

0,17

LINKS

Table of n, a(n) for n=0..77.

FORMULA

Let h(n) = 0, 0, -1, A198442(1), A198442(2), A198442(3), ... Then A(n, 0) = h(n), A(n, 1) = h(n+1) and A(n, k) = A(n, k-2) + n otherwise.

EXAMPLE

The array starts:

[n\k][0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ...]

[0] 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... = A000004

[1] 0, -1, 1, 0, 2, 1, 3, 2, 4, 3, 5, 4, ... = A028242(n-2)

[2] -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ... = A023443(n)

[3] 0, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, ... = 3*A004526(n)

[4] 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, ... = A005843(n)

[5] 2, 3, 7, 8, 12, 13, 17, 18, 22, 23, 27, 28, ... = A047221(n+1)

[6] 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, ... = A008585(n+1)

[7] 6, 8, 13, 15, 20, 22, 27, 29, 34, 36, 41, 43, ... = A047336(n+2)

[8] 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, ... = A008586(n+2)

Successive columns: A198442(n-2), A198442(n-1), A004652(n), A198442(n+1), A198442(n+2), A079524(n), ... .

First subdiagonal: 0, 0, 3, 6, ... = A242477(n).

First upperdiagonal: 0, 1, 2, 6, 10, ... = A238377(n-1).

Array written as a triangle:

0, 0;

0, -1, -1;

0, 1, 0, 0;

0, 0, 1, 0, 0;

0, 2, 2, 3, 2, 2;

etc.

MAPLE

A := proc(n, k) option remember; local h;

h := n -> `if`(n<3, [0, 0, -1][n+1], iquo(n^2-4*n+3, 4));

if k = 0 then h(n) elif k = 1 then h(n+1) else A(n, k-2) + n fi end: # Peter Luschny, Sep 08 2018

MATHEMATICA

h[n_] := If[n < 3, {0, 0, -1}[[n + 1]], Quotient[n^2 - 4 n + 3, 4]];

A[n_, k_] := A[n, k] = If[k == 0, h[n], If[k == 1, h[n+1], A[n, k-2] + n]];

Table[A[n - k, k], {n, 0, 11}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, Jul 22 2019, after Peter Luschny *)

CROSSREFS

Cf. A000004, A004526, A004652, A005843, A008585, A008586, A023443, A028242, A047221, A047336, A079524, A198442, A238377, A242477.

Sequence in context: A097510 A237619 A156747 * A194827 A335359 A332205

Adjacent sequences: A318955 A318956 A318957 * A318959 A318960 A318961

KEYWORD

sign,tabl

AUTHOR

Paul Curtz, Sep 06 2018

STATUS

approved