A265755 a(n) = a(n-1) + a(n-2) if n is even and a(n) = a(n-3) + a(n-4) if n is odd, with a(0) = a(1) = a(2) = 0 and a(3) = 1.

0, 0, 0, 1, 1, 0, 1, 2, 3, 1, 4, 5, 9, 5, 14, 14, 28, 19, 47, 42, 89, 66, 155, 131, 286, 221, 507, 417, 924, 728, 1652, 1341, 2993, 2380, 5373, 4334, 9707, 7753, 17460, 14041, 31501, 25213, 56714, 45542, 102256, 81927, 184183, 147798, 331981, 266110, 598091, 479779, 1077870, 864201, 1942071, 1557649

Offset: 0

Author

Nicholas Drozd, Dec 15 2015

Keywords

• nonn
• easy

Examples

			a(8) = a(7) + a(6)
     = a(4) + a(3) + a(5) + a(4)
     = (a(3) + a(2)) + a(3) + (a(2) + a(1)) + (a(3) + a(2))
     = 1 + 1 + 0 + 1
     = 3
		

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,1,0,2,0,-1).

Crossrefs

Interleaves A006053 and A052547, with an extra leading 0.

A187066 with even values and odd values swapped and an extra leading 0.

Programs

Mathematica

a[0] = a[1] = a[2] = 0; a[3] = 1; a[n_] := a[n] = If[EvenQ@ n, a[n - 1] + a[n - 2], a[n - 3] + a[n - 4]]; Table[a@ n, {n, 0, 55}] (* Michael De Vlieger, Dec 15 2015 *)
nxt[{n_,a_,b_,c_,d_}]:={n+1,b,c,d,If[OddQ[n],c+d,a+b]}; NestList[nxt,{1,0,0,0,1},60][[All,2]] (* or *) LinearRecurrence[{0,1,0,2,0,-1},{0,0,0,1,1,0},60] (* Harvey P. Dale, Nov 10 2017 *)

PARI

concat(vector(3), Vec(x^3*(1+x-x^2)/(1-x^2-2*x^4+x^6) + O(x^70))) \\ Colin Barker, Dec 16 2015

Formula

From Colin Barker, Dec 16 2015: (Start)

a(n) = a(n-2) + 2*a(n-4) - a(n-6) for n>5.

G.f.: x^3*(1+x-x^2) / (1-x^2-2*x^4+x^6).

(End)

Extensions

More terms from Michael De Vlieger, Dec 15 2015