A008496 a(n) = floor(n/5)*floor((n+1)/5)*floor((n+2)/5).

0, 0, 0, 0, 0, 1, 1, 1, 2, 4, 8, 8, 8, 12, 18, 27, 27, 27, 36, 48, 64, 64, 64, 80, 100, 125, 125, 125, 150, 180, 216, 216, 216, 252, 294, 343, 343, 343, 392, 448, 512, 512, 512, 576, 648, 729, 729, 729, 810, 900, 1000

Offset

0,9

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,3,-3,0,0,0,-3,3,0,0,0,1,-1).

Formula

From R. J. Mathar, Apr 16 2010: (Start)

a(n) = A002266(n)*A008497(n+1).

a(n) = a(n-1) +3*a(n-5) -3*a(n-6) -3*a(n-10) +3*a(n-11) +a(n-15) -a(n-16).

G.f.: x^5*(1+x+x^2)*(x^6-x^5+2*x^3-x+1)/((x^4+x^3+x^2+x+1)^3 *(x-1)^4). (End)

Maple

seq( mul(floor((n+j)/5), j=0..2), n=0..55); # G. C. Greubel, Nov 08 2019

Mathematica

LinearRecurrence[{1, 0, 0, 0, 3, -3, 0, 0, 0, -3, 3, 0, 0, 0, 1, -1}, {0, 0, 0, 0, 0, 1, 1, 1, 2, 4, 8, 8, 8, 12, 18, 27}, 60] (* or *) Table[Times@@Thread[Floor[(n +{0, 1, 2} )/5]], {n, 0, 60}] (* Harvey P. Dale, Apr 09 2018 *)
Product[Floor[(Range[55] +j-1)/5], {j, 0, 2}] (* G. C. Greubel, Nov 08 2019 *)

Prog

(PARI) vector(56, n, prod(j=0, 2, (n+j-1)\5) ) \\ G. C. Greubel, Nov 08 2019
(Magma) [&*[Floor((n+j)/5): j in [0..2]]: n in [0..55]]; // G. C. Greubel, Nov 08 2019
(Sage) [product(floor((n+j)/5) for j in (0..2)) for n in (0..55)] # G. C. Greubel, Nov 08 2019
(GAP) List([0..55], n-> Int(n/5)*Int((n+1)/5)*Int((n+2)/5) ); # G. C. Greubel, Nov 08 2019

Crossrefs

Cf. A008382, A008497. - R. J. Mathar, Apr 16 2010

Sequence in context: A083550 A160161 A129279 * A178573 A162794 A172305

Adjacent sequences: A008493 A008494 A008495 * A008497 A008498 A008499

Keyword

nonn

Author

N. J. A. Sloane

Status

approved