A107386 a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4), n>6.

0, 1, 1, 2, 2, 7, 9, 16, 20, 29, 35, 46, 54, 67, 77, 92, 104, 121, 135, 154, 170, 191, 209, 232, 252, 277, 299, 326, 350, 379, 405, 436, 464, 497, 527, 562, 594, 631, 665, 704, 740, 781, 819, 862, 902, 947, 989, 1036, 1080, 1129

Offset: 0

Author

Roger L. Bagula, May 24 2005, corrected Sep 04 2008

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Crossrefs

Cf. A107387, A107388, A107389.

Programs

Mathematica

Clear[M, m, v, aa] (*A107386*)m = 2; M = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, m, 0, - m}};Expand[Det[M - x*IdentityMatrix[4]]] ;NSolve[Det[M - x*IdentityMatrix[4]] == 0, x] ;v[1] = {0, 1, 1, 2}; v[n_] := v[n] = M . v[n - 1]; digits = 50; aa = Table[Abs[v[n][[1]]], {n, 1, digits}]
a=2; lst={0, 1, 1, a}; Do[a=n^2-a; AppendTo[lst, a], {n, 2, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 17 2008 *)
LinearRecurrence[{2,0,-2,1},{0,1,1,2,2,7,9},50] (* Harvey P. Dale, Dec 07 2021 *)

Formula

For n>=4, a(n) = (n-2)^2 - a(n-1). - Alex Ratushnyak, Aug 03 2012

G.f.: x*(-4*x^4+2*x^5+x-1)/((1+x)*(x-1)^3). - N. J. A. Sloane, Sep 28 2009

a(n)= n^2/2-3*n/2+1-(-1)^n, n>2. - N. J. A. Sloane, Sep 28 2009

Extensions

Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009