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
Keywords
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).
Crossrefs
Programs
-
GAP
List([0..55], n-> Int(n/5)*Int((n+1)/5)*Int((n+2)/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
-
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 *) -
PARI
vector(56, n, prod(j=0,2, (n+j-1)\5) ) \\ 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
Formula
From R. J. Mathar, Apr 16 2010: (Start)
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)