A064835 If n mod 2 = 0 then a(n) = n^4/4 - 2*n^2 + 3*n; otherwise, a(n) = n^4/4 - 2*n^2 + 3*n - 5/4.

0, 0, 2, 10, 44, 120, 270, 522, 920, 1504, 2330, 3450, 4932, 6840, 9254, 12250, 15920, 20352, 25650, 31914, 39260, 47800, 57662, 68970, 81864, 96480, 112970, 131482, 152180, 175224, 200790, 229050, 260192, 294400, 331874, 372810, 417420, 465912, 518510, 575434

Offset

0,3

Links

Harry J. Smith, Table of n, a(n) for n = 0..1000

G. L. Cohen and E. Tonkes, Dartboard arrangements, Elect. J. Combin., 8 (No. 2, 2001), #R4.

Index entries for linear recurrences with constant coefficients, signature (4,-5,0,5,-4, 1).

Formula

G.f.: 2*x^2*(1+x+7*x^2-3*x^3)/((1-x)^5*(1+x)). - Colin Barker, Apr 20 2012

a(n) = 4*a(n-1) - 5*a(n-2) + 5*a(n-4) - 4*a(n-5) + a(n-6). - Vincenzo Librandi, Jun 19 2018

Mathematica

Table[If[EvenQ[n], n^4/4-2n^2+3n, n^4/4-2n^2+3n-5/4], {n, 0, 40}] (* Harvey P. Dale, Dec 02 2014 *)
LinearRecurrence[{4, -5, 0, 5, -4, 1}, {0, 0, 2, 10, 44, 120}, 40] (* Vincenzo Librandi, Jun 19 2018 *)

Prog

(PARI) a(n) = { (n^4/4 - 2*n^2 + 3*n) - if (n%2, 5/4, 0) } \\ Harry J. Smith, Sep 28 2009
(PARI) a(n) = n^4\4 - 2*n^2 + 3*n - n%2 \\ Charles R Greathouse IV, Dec 29 2024
(Magma) I:=[0, 0, 2, 10, 44, 120]; [n le 6 select I[n] else 4*Self(n-1) - 5*Self(n-2) + 5*Self(n-4) - 4*Self(n-5) + Self(n-6): n in [1..40]]; // Vincenzo Librandi, Jun 19 2018

Crossrefs

Cf. A064836.

Sequence in context: A376225 A005144 A305657 * A225958 A240377 A025590

Adjacent sequences: A064832 A064833 A064834 * A064836 A064837 A064838

Keyword

nonn,easy

Author

N. J. A. Sloane, Oct 25 2001

Status

approved