A259968 - OEIS

%I #31 Jan 28 2025 17:13:08

%S 1,1,3,6,10,17,30,53,93,163,286,502,881,1546,2713,4761,8355,14662,

%T 25730,45153,79238,139053,244021,428227,751486,1318766,2314273,

%U 4061266,7127025,12507057,21948355,38516678,67592058,118615793,208156206,365288677,641036941

%N a(n) = a(n-1) + a(n-2) + a(n-4), with a(1)=1, a(2)=1, a(3)=3, a(4)=6.

%D R. K. Guy, Letter to N. J. A. Sloane, Feb 05 1986.

%H Colin Barker, <a href="/A259968/b259968.txt">Table of n, a(n) for n = 1..1000</a>

%H R. K. Guy, <a href="/A005251/a005251.pdf">Letter to N. J. A. Sloane, Feb 1986</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,1).

%F G.f.: -x*(2*x^2-x+1) / (x^3-x^2+2*x-1). - _Colin Barker_, Jul 12 2015

%t LinearRecurrence[{1, 1, 0, 1}, {1, 1, 3, 6}, 40] (* _Vincenzo Librandi_, Jul 12 2015 *)

%t nxt[{a_,b_,c_,d_}]:={b,c,d,a+c+d}; NestList[nxt,{1,1,3,6},40][[;;,1]] (* _Harvey P. Dale_, Jan 28 2025 *)

%o (Magma) I:=[1,1,3,6]; [n le 4 select I[n] else Self(n-1)+Self(n-2)+Self(n-4): n in [1..40]]; // _Vincenzo Librandi_, Jul 12 2015

%o (PARI) Vec(-x*(2*x^2-x+1)/(x^3-x^2+2*x-1) + O(x^50)) \\ _Colin Barker_, Jul 12 2015

%o (Haskell)

%o a259968 n = a259968_list !! n

%o a259968_list = 1 : 1 : 3 : 6 : zipWith3 (((+) .) . (+))

%o    a259968_list (drop 2 a259968_list) (drop 3 a259968_list)

%o -- _Reinhard Zumkeller_, Jul 12 2015

%Y Cf. A259969, A259967.

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_, Jul 11 2015

%E a(28)-a(37) from _Hiroaki Yamanouchi_, Jul 12 2015