A214272 Number of compositions of n where the difference between largest and smallest parts equals 3 and adjacent parts are unequal.

0, 2, 1, 8, 12, 18, 46, 69, 111, 208, 340, 539, 910, 1497, 2403, 3924, 6331, 10230, 16531, 26591, 42652, 68595, 110195, 176458, 282895, 452990, 725036, 1160067, 1855376, 2966265, 4740385, 7574822, 12099506, 19324253, 30856321, 49260709, 78631609, 125495919

Offset

4,2

Links

Alois P. Heinz, Table of n, a(n) for n = 4..2000

Formula

a(n) ~ c * d^n, where d = 1.59406371344091594038982448... is the root of the equation -3 + d - 3*d^2 - 3*d^4 + d^5 - 2*d^6 + d^7 - d^8 + d^9 = 0, and c = 0.63168955798354197444724247228159886565558573072349896252... . - Vaclav Kotesovec, Sep 01 2014

Example

T(5) = 2: [4,1], [1,4].
T(6) = 1: [1,4,1].
T(7) = 8: [5,2], [4,2,1], [4,1,2], [2,5], [2,4,1], [2,1,4], [1,4,2], [1,2,4].
T(8) = 12: [4,3,1], [4,1,3], [4,1,2,1], [3,4,1], [3,1,4], [2,1,4,1], [1,4,3], [1,4,2,1], [1,4,1,2], [1,3,4], [1,2,4,1], [1,2,1,4].

Crossrefs

Column k=3 of A214269.

Sequence in context: A118708 A055134 A137370 * A214273 A214274 A214275

Adjacent sequences: A214269 A214270 A214271 * A214273 A214274 A214275

Keyword

nonn

Author

Alois P. Heinz, Jul 09 2012

Status

approved