A360665 - OEIS

A360665

Square array T(n, k) = k*((2*n-1)*k+1)/2 read by rising antidiagonals.

0, 0, 0, 0, 1, -1, 0, 2, 3, -3, 0, 3, 7, 6, -6, 0, 4, 11, 15, 10, -10, 0, 5, 15, 24, 26, 15, -15, 0, 6, 19, 33, 42, 40, 21, -21, 0, 7, 23, 42, 58, 65, 57, 28, -28, 0, 8, 27, 51, 74, 90, 93, 77, 36, -36, 0, 9, 31, 60, 90, 115, 129, 126, 100, 45, -45

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,8

LINKS

Table of n, a(n) for n=0..65.

FORMULA

T(n,k) = T(n,k-1)+k^2.

T(n,n) = A081436(n-1).

T(n,n+1) = A059270(n).

T(n,n+4) = -3*A179297(n+4).

T(n+3,n) = A162254(n).

T(n+5,n) = 3*A101986(n).

From Stefano Spezia, Mar 31 2023: (Start)

O.g.f.: (x*y - y^2 + 2*x*y^2)/((1 - x)^2*(1 - y)^3).

E.g.f.: exp(x+y)*y*(2*x - y + 2*x*y)/2. (End)

EXAMPLE

By rows:

0, 0, -1, -3, -6, -10, -15, -21, -28, ... = -A161680

0, 1, 3, 6, 10, 15, 21, 28, 36, ... = A000217

0, 2, 7, 15, 26, 40, 57, 77, 100, ... = A005449

0, 3, 11, 24, 42, 65, 93, 126, 164, ... = A005475

0, 4, 15, 33, 58, 90, 129, 175, 228, ... = A022265

0, 5, 19, 42, 74, 115, 165, 224, 292, ... = A022267

0, 6, 23, 51, 90, 140, 201, 273, 356, ... = A022269

... .

MATHEMATICA

T[n_, k_] := ((2*n - 1)*k^2 + k)/2; Table[T[n - k, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Amiram Eldar, Mar 31 2023 *)

PROG

(PARI) T(n, k) = ((2*n-1)*k^2+k)/2 \\ Thomas Scheuerle, Mar 17 2023

CROSSREFS

Cf. Antidiagonal sums: A034827(n+1).

Cf. A000217, A000290, A005449, A005475, A022265.

Cf. A022267, A022269, A059270, A081436, A101986.

Cf. A161680, A162254, A179297, A360962, A361226.

Sequence in context: A087401 A332915 A192498 * A308178 A127572 A021815

Adjacent sequences: A360662 A360663 A360664 * A360666 A360667 A360668

KEYWORD

sign,tabl,easy

AUTHOR

Paul Curtz, Mar 17 2023

STATUS

approved