The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A287326 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A287326

Triangle read by rows: T(n, k) = 6*k*(n-k) + 1; n >= 0, 0 <= k <= n.
(history; published version)

#438 by Peter Luschny at Fri Sep 27 05:44:21 EDT 2024

STATUS

reviewed

approved

#437 by Joerg Arndt at Fri Sep 27 02:02:51 EDT 2024

STATUS

proposed

reviewed

#436 by Stefano Spezia at Wed Sep 25 02:16:23 EDT 2024

STATUS

editing

proposed

#435 by Stefano Spezia at Wed Sep 25 02:15:56 EDT 2024

FORMULA

G.f.: (1 - 8*y - 5*y^2 - x*(1 - 14x*y + y7*x^2)*y)/((1 - x)^2*(1 - x*y)^32). - Stefano Spezia, Oct 09 2018 [Adapted by _Stefano Spezia_, Sep 25 2024]

STATUS

proposed

editing

#434 by G. C. Greubel at Wed Sep 25 01:43:14 EDT 2024

STATUS

editing

proposed

#433 by G. C. Greubel at Wed Sep 25 01:41:57 EDT 2024

FORMULA

Sum_{k=0..n} (-1)^k*T(n, k) = (-1/2)*(1 + (-1)^n)*A016969(1 - 6*floor(n/2) - 1). - G. C. Greubel, Sep 25 2024

CROSSREFS

Cf. A000124, A000578, A003154, A003215, A007318, A008458, A038593, A055012, A068601, A077028, A094053, A166873, A227776, A294317, A302971, A304042A016969.

Cf. A038593, A055012, A068601, A077028, A094053, A166873, A227776.

Cf. A294317, A302971, A304042.

STATUS

proposed

editing

Discussion

Wed Sep 25

01:43

G. C. Greubel: Yes; Thanks for the help.

#432 by Michel Marcus at Wed Sep 25 01:35:53 EDT 2024

STATUS

editing

proposed

#431 by Michel Marcus at Wed Sep 25 01:35:10 EDT 2024

FORMULA

From Kolosov Petro, Jun 05 2019 : (Start):

STATUS

proposed

editing

Discussion

Wed Sep 25

01:35

Michel Marcus: new formula gives 1, 0, -5, 0, -11, 0, -17, 0, -23, ... so see A016969 ?

#430 by G. C. Greubel at Wed Sep 25 01:27:16 EDT 2024

STATUS

editing

proposed

#429 by G. C. Greubel at Wed Sep 25 01:26:52 EDT 2024

COMMENTS

T(n, k) is symmetric: T(n, k) = T(n, n-k). (End)

(End)

Sum_{k=0..n} (-1)^k*T(n, k) = (1/2)*(1 + (-1)^n)*(1 - 6*floor(n/2)). - G. C. Greubel, Sep 25 2024

FORMULA

G.f.: (-1 + - 8*y + - 5*y^2 + - x*(1 - 14*y + y^2))/((-1 + - x)^2*(-1 + - y)^3). - Stefano Spezia, Oct 09 2018

Sum_{k=0..n} (-1)^k*T(n, k) = (1/2)*(1 + (-1)^n)*(1 - 6*floor(n/2)). - G. C. Greubel, Sep 25 2024