A267807 a(0) = a(1) = 1; for n>1, a(n) = (a(n-1) mod 3) + a(n-2).

1, 1, 2, 3, 2, 5, 4, 6, 4, 7, 5, 9, 5, 11, 7, 12, 7, 13, 8, 15, 8, 17, 10, 18, 10, 19, 11, 21, 11, 23, 13, 24, 13, 25, 14, 27, 14, 29, 16, 30, 16, 31, 17, 33, 17, 35, 19, 36, 19, 37, 20, 39, 20, 41, 22, 42, 22, 43, 23, 45, 23, 47, 25, 48, 25, 49, 26, 51, 26, 53, 28

Offset

0,3

Links

Table of n, a(n) for n=0..70.

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

Formula

G.f.: (1 + x + x^2 + 2*x^3 + 2*x^5 + 2*x^6 + x^7 - x^8)/((1 - x)^2*(1 + x)^2* (1 + x^2)*(1 + x^4)). [Bruno Berselli, Jan 21 2016]

a(n) = a(n-2) + a(n-8) - a(n-10) for n>9. [Bruno Berselli, Jan 21 2016]

Mathematica

RecurrenceTable[{a[0] == a[1] == 1, a[n] == Mod[a[n - 1], 3] + a[n - 2]}, a, {n, 90}]
LinearRecurrence[{0, 1, 0, 0, 0, 0, 0, 1, 0, -1}, {1, 1, 2, 3, 2, 5, 4, 6, 4, 7}, 90] (* Bruno Berselli, Jan 21 2016 *)

Prog

(PARI) a=vector(100); for(n=1, #a, if(n<3, a[n]=1, a[n]=a[n-1]%3+a[n-2])); a \\ Colin Barker, Jan 22 2016

Crossrefs

Cf. A000045, A267806, A267808, A267809.

Sequence in context: A210221 A232113 A216475 * A127433 A055573 A238729

Adjacent sequences: A267804 A267805 A267806 * A267808 A267809 A267810

Keyword

nonn,easy

Author

José María Grau Ribas, Jan 20 2016

Extensions

Edited by Bruno Berselli, Jan 21 2016

Status

approved