The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A213482

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A213482

Number of (w,x,y) with all terms in {0,...,n} and |w-x| + |x-y| > w+x+y.
(history; published version)

#20 by Michael De Vlieger at Fri Dec 31 09:56:18 EST 2021

STATUS

reviewed

approved

#19 by Michel Marcus at Fri Dec 31 02:25:56 EST 2021

STATUS

proposed

reviewed

#18 by Jon E. Schoenfield at Wed Dec 29 21:21:36 EST 2021

STATUS

editing

proposed

#17 by Jon E. Schoenfield at Wed Dec 29 21:21:31 EST 2021

NAME

Number of (w,x,y) with all terms in {0,...,n} and |w-x| + |x-y| > w+x+y.

FORMULA

a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6).

G.f.: (3*x + 8*x^2 + 10*x^3 + 3*x^4 - x^5)/((1 - x)^4 (1 + x)^2)).

STATUS

reviewed

editing

#16 by Andrew Howroyd at Wed Dec 29 13:59:57 EST 2021

STATUS

proposed

reviewed

#15 by Michel Marcus at Wed Dec 29 01:17:20 EST 2021

STATUS

editing

proposed

#14 by Michel Marcus at Wed Dec 29 01:17:18 EST 2021

COMMENTS

a(n)+A213483 = (n+1)^3.

FORMULA

a(n) + A213483(n) = (n+1)^3.

From Ayoub Saber Rguez, Dec 29 2021 : (Start)

a(n) = A213481(n) - A213479(n).

a(n) = (23*n^3 + 39*n^2 + n + 9 - (3*n+9)*((n+1) mod 2))/24. (End)

CROSSREFS

Cf. A212959, A213479, A213481, A213483.

STATUS

proposed

editing

#13 by Ayoub Saber Rguez at Tue Dec 28 22:45:03 EST 2021

STATUS

editing

proposed

Discussion

Tue Dec 28

22:46

Ayoub Saber Rguez: I simplified the formula

#12 by Ayoub Saber Rguez at Tue Dec 28 22:44:15 EST 2021

FORMULA

a(n)= (23*n^3 + 39*n^2 + 4*n + 15 9 - (3*n+6)*(n mod 2) - (6*n+159)*((n+1) mod 2))/24. (End)

STATUS

proposed

editing

#11 by Andrew Howroyd at Tue Dec 28 19:44:01 EST 2021

STATUS

editing

proposed