A267808 a(0) = a(1) = 1; for n>1, a(n) = (a(n-1) mod 4) + a(n-2).

1, 1, 2, 3, 5, 4, 5, 5, 6, 7, 9, 8, 9, 9, 10, 11, 13, 12, 13, 13, 14, 15, 17, 16, 17, 17, 18, 19, 21, 20, 21, 21, 22, 23, 25, 24, 25, 25, 26, 27, 29, 28, 29, 29, 30, 31, 33, 32, 33, 33, 34, 35, 37, 36, 37, 37, 38, 39, 41, 40, 41, 41, 42, 43, 45, 44, 45, 45, 46, 47, 49

Offset

0,3

Links

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

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

Formula

From Bruno Berselli, Jan 21 2016: (Start)

G.f.: (1 + x^2 + x^3 + 2*x^4 - x^5) / ((1 + x)*(1 - x)^2*(1 - x + x^2)*(1 + x + x^2)).

a(n) = a(n-1) + a(n-6) - a(n-7) for n>6.

a(n) = n - floor((n+1)/3) + ((-1)^n - (-1)^(floor(n/3)))/2 + 1. (End)

Mathematica

RecurrenceTable[{a[0] == a[1] == 1, a[n] == Mod[a[n - 1], 4] + a[n - 2]}, a, {n, 70}]
Table[n - Floor[(n + 1)/3] + ((-1)^n - (-1)^Floor[n/3])/2 + 1, {n, 0, 70}] (* or *) LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {1, 1, 2, 3, 5, 4, 5}, 80] (* 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]%4+a[n-2])); a \\ Colin Barker, Jan 22 2016

Crossrefs

Cf. A000045, A267806, A267807, A267809.

Sequence in context: A104204 A131296 A371216 * A239852 A263279 A262507

Adjacent sequences: A267805 A267806 A267807 * A267809 A267810 A267811

Keyword

nonn,easy

Author

José María Grau Ribas, Jan 20 2016

Extensions

Edited by Bruno Berselli, Jan 21 2016.

Status

approved