A038715 a(n) = floor(n/4)*ceiling((n+2)/4).

0, 0, 0, 0, 2, 2, 2, 3, 6, 6, 6, 8, 12, 12, 12, 15, 20, 20, 20, 24, 30, 30, 30, 35, 42, 42, 42, 48, 56, 56, 56, 63, 72, 72, 72, 80, 90, 90, 90, 99, 110, 110, 110, 120, 132, 132, 132, 143, 156, 156, 156, 168, 182, 182, 182, 195, 210, 210, 210, 224, 240

Offset

0,5

Comments

The three fixed points of this sequence are 0, 12 and 15. - Bernard Schott, Feb 27 2023

Links

Table of n, a(n) for n=0..60.

Index entries for linear recurrences with constant coefficients, signature (2,-2,2,0,-2,2,-2,1).

Formula

a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - 2*a(n-5) + 2*a(n-6) - 2*a(n-7) + a(n-8). - R. J. Mathar, Mar 11 2012

a(n) = A002265(n)*A002265(n+5). - Michel Marcus, Feb 27 2023

From Amiram Eldar, Mar 04 2023: (Start)

Sum_{n>=4} 1/a(n) = 15/4.

Sum_{n>=4} (-1)^n/a(n) = 1/4. (End)

Maple

Sequence = seq(floor(n/4)*ceiling((n+2)/4), n=0..60); # Bernard Schott, Mar 01 2023

Mathematica

LinearRecurrence[{2, -2, 2, 0, -2, 2, -2, 1}, {0, 0, 0, 0, 2, 2, 2, 3}, 80] (* Harvey P. Dale, Nov 05 2014 *)

Prog

(Python)
def A038715(n): return (n>>2)*(1+(n+1>>2)) # Chai Wah Wu, Feb 02 2023
(PARI) a(n) = (n\4)*((n+5)\4); \\ Michel Marcus, Feb 27 2023

Crossrefs

Cf. A002265.

Sequence in context: A104856 A306393 A324763 * A293518 A057040 A363772

Adjacent sequences: A038712 A038713 A038714 * A038716 A038717 A038718

Keyword

nonn

Author

N. J. A. Sloane, May 02 2000

Status

approved