A271970 Linear recurrence, with both signature and original terms = 1,0,1,0,1

1, 0, 1, 0, 1, 3, 3, 5, 8, 12, 20, 31, 48, 76, 119, 187, 294, 461, 724, 1137, 1785, 2803, 4401, 6910, 10850, 17036, 26749, 42000, 65946, 103545, 162581, 255276, 400821, 629348, 988169, 1551571, 2436195, 3825185, 6006104, 9430468, 14807224, 23249523, 36505176

Offset

1,6

Links

Table of n, a(n) for n=1..43.

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

Formula

a(1)=1, a(2)=0, a(3)=1, a(4)=0, a(5)=1, a(n)=a(n-1)+a(n-3)+a(n-5).

G.f.: ( -x*(x-1)*(x^3-x^2-1) ) / ( -1+x+x^3+x^5 ). - R. J. Mathar, Apr 17 2016

a(n) = A060961(n) -A060961(n-2) -2*A060961(n-4). - R. J. Mathar, Apr 17 2016

Mathematica

With[{c={1, 0, 1, 0, 1}}, LinearRecurrence[c, c, 100]]

Crossrefs

Sequence in context: A336132 A200737 A200741 * A213678 A293676 A303714

Adjacent sequences: A271967 A271968 A271969 * A271971 A271972 A271973

Keyword

nonn,easy

Author

Harvey P. Dale, Apr 17 2016

Status

approved