OFFSET
1,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).
FORMULA
From R. J. Mathar, Jul 10 2009: (Start)
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) = 5/8 - 3n/2 + 9n^2/4 + 3*(-1)^n/8.
G.f.: x*(1+5*x+2*x^2+x^3)/((1+x)*(1-x)^3). (End)
MAPLE
A121410 := proc(nmin) local M, a, v, wev, wod, n ; a := [] ; M := linalg[matrix](2, 2, [0, 1, -1, 2]) ; v := linalg[vector](2, [1, 7]) ; wev := linalg[vector](2, [0, 3]) ; wod := linalg[vector](2, [0, 6]) ; while nops(a) < nmin do a := [op(a), v[1]] ; n := nops(a)+1 ; v := evalm(M &* v) ; if n mod 2 = 0 then v := evalm(v+wev) ; else v := evalm(v+wod) ; fi ; od: RETURN(a) ; end: A121410(80) ; # R. J. Mathar, Sep 18 2007
MATHEMATICA
M := {{0, 1}, {-1, 2} } v[1] = {1, 7} w[n_] = If[Mod[n, 2] == 0, {0, 3}, {0, 6}] v[n_] := v[n] = M.v[n - 1] + w[n] a = Table[v[n][[1]], {n, 1, 30}]
CoefficientList[Series[x (1+5x+2x^2+x^3)/((1+x)(1-x)^3), {x, 0, 50}], x] (* or *) LinearRecurrence[{2, 0, -2, 1}, {1, 7, 16, 31}, 50] (* Harvey P. Dale, Mar 10 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Sep 07 2006
EXTENSIONS
Edited by N. J. A. Sloane, Sep 16 2006
More terms from R. J. Mathar, Sep 18 2007
New name from Joerg Arndt, Jun 28 2013
STATUS
approved