A239905 If n <= 5 then a(n) = 1, if 6 <= n <= 8 then 2, if n = 9 or 10 then 3, if n = 11, 12 or 13 then n-7; otherwise a(n) = 2*a(n - 4) + a(n - 12).

1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 6, 7, 9, 11, 13, 16, 20, 24, 29, 35, 44, 53, 64, 77, 97, 117, 141, 170, 214, 258, 311, 375, 472, 569, 686, 827, 1041, 1255, 1513, 1824, 2296, 2768, 3337, 4023, 5064, 6105, 7360, 8873, 11169, 13465, 16233, 19570, 24634, 29698, 35803, 43163, 54332, 65501

Offset

1,6

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

R. S. Booth, An odd order search problem, SIAM J. Algebraic Discrete Methods 3 (1982), no. 1, 135--143. MR0644964 (83d:90106). See sequence U(n).

Index entries for linear recurrences with constant coefficients, signature (0,0,0,2,0,0,0,0,0,0,0,1).

Formula

G.f.: x*(x^12-x^11+x^9-x^8+x^4-x^3-x^2-x-1) / (x^12+2*x^4-1). - Colin Barker, Apr 18 2014

Maple

U:=proc(n) option remember; if n <= 5 then 1
elif n <= 8 then 2
elif n <= 10 then 3
elif n = 11 then 4
elif n = 12 then 5
elif n = 13 then 6
else 2*U(n-4)+U(n-12); fi; end;
[seq(U(n), n=1..60)];

Mathematica

CoefficientList[Series[(x^12 - x^11 + x^9 - x^8 + x^4 - x^3 - x^2 - x - 1)/(x^12 + 2 x^4 - 1), {x, 0, 40}], x] (* Vincenzo Librandi, Apr 19 2014 *)
LinearRecurrence[{0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 6}, 70] (* Harvey P. Dale, Mar 30 2019 *)

Crossrefs

Sequence in context: A120170 A136421 A274159 * A016085 A018122 A074732

Adjacent sequences: A239902 A239903 A239904 * A239906 A239907 A239908

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 07 2014

Status

approved