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

0,4

Links

Table of n, a(n) for n=0..49.

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

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

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 *)

Crossrefs

Cf. A107387, A107388, A107389.

Sequence in context: A070910 A189040 A267214 * A095021 A347913 A348532

Adjacent sequences: A107383 A107384 A107385 * A107387 A107388 A107389

Keyword

nonn,easy

Author

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

Extensions

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

Status

approved