A131761 a(3n) = 3a(3n-1)-3a(3n-2)+2a(3n-3), a(3n+1) = 3a(3n)-3a(3n-1)+2a(3n-2), a(3n+2) = 3a(3n+1)-3a(3n), a(0) = 0, a(1) = 1, a(2) = 2.

0, 1, 2, 3, 5, 6, 9, 19, 30, 51, 101, 150, 249, 499, 750, 1251, 2501, 3750, 6249, 12499, 18750, 31251, 62501, 93750, 156249, 312499, 468750, 781251, 1562501, 2343750, 3906249, 7812499, 11718750, 19531251, 39062501, 58593750, 97656249, 195312499, 292968750

Offset

0,3

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,-1,5,-5,5).

Formula

a(n) = a(n-1)-a(n-2)+5*a(n-3)-5*a(n-4)+5*a(n-5) for n>7. - Colin Barker, Nov 04 2014

G.f.: x*(x+1)*(4*x^5-2*x^4+3*x^3-2*x^2-1) / ((x^2-x+1)*(5*x^3-1)). - Colin Barker, Nov 04 2014

Mathematica

LinearRecurrence[{1, -1, 5, -5, 5}, {0, 1, 2, 3, 5, 6, 9, 19}, 40] (* Harvey P. Dale, May 13 2022 *)

Prog

(PARI) concat(0, Vec(x*(x+1)*(4*x^5-2*x^4+3*x^3-2*x^2-1)/((x^2-x+1)*(5*x^3-1)) + O(x^100))) \\ Colin Barker, Nov 04 2014

Crossrefs

Sequence in context: A124253 A256230 A079371 * A272776 A055690 A108861

Adjacent sequences: A131758 A131759 A131760 * A131762 A131763 A131764

Keyword

nonn,easy

Author

Paul Curtz, Oct 23 2007

Extensions

More terms from Colin Barker, Nov 04 2014

Status

approved