A117652 a(n) = floor(n*(n+2)*(n+4)*(n-6)/192).

0, -1, -1, -2, -2, -2, 0, 3, 10, 20, 35, 55, 84, 120, 168, 227, 300, 388, 495, 621, 770, 943, 1144, 1374, 1638, 1937, 2275, 2654, 3080, 3553, 4080, 4662, 5304, 6009, 6783, 7628, 8550, 9552, 10640, 11817, 13090, 14462, 15939, 17525, 19228, 21050, 23000, 25081

Offset: 0

Author

Roger L. Bagula, Apr 11 2006

Keywords

• sign
• easy

Comments

Quasipolynomial with period 16. - Charles R Greathouse IV, Sep 06 2011

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (4,-5,0,4,0,-4,0,4,0,-4,0,4,0,-4,0,5,-4,1).

Crossrefs

Cf. A052472, A018226.

Programs

Magma

[Floor( n*(n+2)*(n+4)*(n-6)/192): n in [0..50]]; // Vincenzo Librandi, Sep 06 2011

Mathematica

Table[Floor[n*(n+1)*(n+2)*(n-3)/12], {n, 0, 25, 1/2}]
LinearRecurrence[{4,-5,0,4,0,-4,0,4,0,-4,0,4,0,-4,0,5,-4,1},{0,-1,-1,-2,-2,-2,0,3,10,20,35,55,84,120,168,227,300,388},50] (* Harvey P. Dale, Nov 02 2024 *)

PARI

a(n)=n*(n+2)*(n+4)*(n-6)\192 \\ Charles R Greathouse IV, Sep 06 2011

Sage

[floor(n*(n+2)*(n+4)*(n-6)/192) for n in (0..50)] # G. C. Greubel, May 20 2019

Formula

a(n) = floor( n*(n+2)*(n+4)*(n-6)/192).

a(n) = 4*a(n-1) - 5*a(n-2) + 4*a(n-4) - 4*a(n-6) + 4*a(n-8) - 4*a(n-10) + 4*a(n-12) - 4*a(n-14) + 5*a(n-16) - 4*a(n-17) + a(n-18).

Extensions

More precise description, converted to a more regular signed sequence - the Assoc. Eds. of the OEIS, Jun 27 2010