A093391 a(n) = floor(n/16) + floor((n+1)/16) + floor((n+2)/16) + floor((n+3)/16).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 6, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 10, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 14, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 18, 19, 20, 20, 20, 20

Offset: 0

Author

Reinhard Zumkeller, Mar 28 2004

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,-1,0,-1,2,-1,0,-1,2,-1,0,-1,2,-1).

Crossrefs

Cf. A004524, A093390, A093392.

Cf. A054900.

Programs

Haskell

a093391 n = sum $ map ((flip div 16) . (+ n)) [0..3] -- Reinhard Zumkeller, Oct 10 2013

Magma

[Floor(n/16)+Floor((n+1)/16)+Floor((n+2)/16)+Floor((n+3)/16): n in [0..100]]; // Vincenzo Librandi, Feb 16 2018

Mathematica

Total/@(Floor/@(Partition[Range[0,90],4,1]/16)) (* Harvey P. Dale, Sep 21 2013 *)
CoefficientList[Series[x^13 / ((1 + x^4) (x^8 + 1) (x - 1)^2), {x, 0, 100}], x] (* Vincenzo Librandi, Feb 16 2018 *)

PARI

a(n) = n\16 + (n+1)\16 + (n+2)\16 + (n+3)\16 \\ Andrew Howroyd, Feb 15 2018

Formula

From R. J. Mathar, Mar 22 2011: (Start)

a(n) = +2*a(n-1) -a(n-2) -a(n-4) +2*a(n-5) -a(n-6) -a(n-8) +2*a(n-9) -a(n-10) -a(n-12) +2*a(n-13) -a(n-14).

G.f.: x^13/ ( (1+x^4)*(x^8+1)*(x-1)^2 ).

(End)