A276276 a(n) = a(n-2)+a(n-3) with a(1)=2 a(2)=1 a(3)=0.

2, 1, 0, 3, 1, 3, 4, 4, 7, 8, 11, 15, 19, 26, 34, 45, 60, 79, 105, 139, 184, 244, 323, 428, 567, 751, 995, 1318, 1746, 2313, 3064, 4059, 5377, 7123, 9436, 12500, 16559, 21936, 29059, 38495, 50995, 67554, 89490

Offset: 1

Author

Nicolas Bègue, Aug 26 2016

Keywords

• nonn
• easy

Comments

Sequence is obtained from modulo 3 periodic sequence of Padovan numbers 1112201210010, it satisfies the same recurrence a(n) = a(n-2) + a(n-3).

Links

• Index entries for linear recurrences with constant coefficients, signature (0,1,1).

Crossrefs

Cf. A000931, A060006.

Programs

Mathematica

RecurrenceTable[{a[n] == a[n - 2] + a[n - 3], a[1] == 2, a[2] == 1, a[3] == 0}, a, {n, 1, 43}] (* or *)
CoefficientList[Series[(2 x^2 - x - 2)/(x^3 + x^2 - 1), {x, 0, 42}], x] (* Michael De Vlieger, Aug 28 2016 *)

PARI

a(n)=([0,1,0; 0,0,1; 1,1,0]^(n-1)*[2;1;0])[1,1] \\ Charles R Greathouse IV, Aug 28 2016

Formula

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

a(n) = A000931(n) - A000931(n-9), for n>2.

Extensions

More terms from Charles R Greathouse IV, Aug 28 2016