A173711 Nonnegative integers, six even followed by two odd.

0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 16, 16, 16, 16, 16, 16, 17, 17

Offset: 0

Author

Adriano Caroli, Nov 25 2010

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1,-1,1,1,-1).

Programs

Magma

I:=[0,0,0,0,0,0,1]; [n le 7 select I[n] else Self(n-1) + Self(n-2) - Self(n-3)-Self(n-4)+Self(n-5)+Self(n-6)-Self(n-7): n in [1..80]]; // Vincenzo Librandi, Nov 24 2016

Mathematica

LinearRecurrence[{1,1,-1,-1,1,1,-1},{0,0,0,0,0,0,1},50] (* G. C. Greubel, Nov 23 2016 *)
CoefficientList[Series[x^6 / ((x + 1) (x^4 + 1) (x - 1)^2), {x, 0, 100}], x] (* Vincenzo Librandi, Nov 24 2016 *)
Table[If[EvenQ[n],PadRight[{},6,n],{n,n}],{n,0,20}]//Flatten (* Harvey P. Dale, Nov 07 2020 *)

Formula

a(n) = A180969(3,n) + A180969(3,n+2).

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

a(n) = a(n-1) + a(n-2) - a(n-3) - a(n-4) + a(n-5) + a(n-6) - a(n-7). - G. C. Greubel, Nov 23 2016