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

0,8

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).

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)

Example

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

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 *)

Prog

(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

Crossrefs

Interleaves A006053 and A052547, with an extra leading 0.

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

Sequence in context: A305433 A257681 A338240 * A341130 A330139 A349358

Adjacent sequences: A265752 A265753 A265754 * A265756 A265757 A265758

Keyword

nonn,easy

Author

Nicholas Drozd, Dec 15 2015

Extensions

More terms from Michael De Vlieger, Dec 15 2015

Status

approved