A214273 Number of compositions of n where the difference between largest and smallest parts equals 4 and adjacent parts are unequal.

0, 2, 1, 8, 12, 23, 51, 90, 165, 295, 550, 952, 1682, 2974, 5151, 9007, 15530, 26848, 46194, 79404, 136092, 232622, 397633, 677892, 1154741, 1964078, 3337218, 5664428, 9605090, 16274305, 27548925, 46602325, 78775262, 133073729, 224662007, 379067097, 639250682

Offset

5,2

Links

Alois P. Heinz, Table of n, a(n) for n = 5..2000

Formula

a(n) ~ c * d^n, where d = 1.67058061397048614428193473494469299002584... is the root of the equation -4 + 5*d - 9*d^2 + 8*d^3 - 12*d^4 + 9*d^5 - 11*d^6 + 8*d^7 - 9*d^8 + 6*d^9 - 5*d^10 + 3*d^11 - 2*d^12 + d^13 = 0, c = 0.5575332183681935160094360162291847580554... . - Vaclav Kotesovec, Sep 01 2014

Example

a(6) = 2: [5,1]. [1,5].
a(7) = 1: [1,5,1].
a(8) = 8: [6,2], [5,2,1], [5,1,2], [2,6], [2,5,1], [2,1,5], [1,5,2], [1,2,5].
a(9) = 12: [5,3,1], [5,1,3], [5,1,2,1], [3,5,1], [3,1,5], [2,1,5,1], [1,5,3], [1,5,2,1], [1,5,1,2], [1,3,5], [1,2,5,1], [1,2,1,5].

Crossrefs

Column k=4 of A214269.

Sequence in context: A055134 A137370 A214272 * A214274 A214275 A214276

Adjacent sequences: A214270 A214271 A214272 * A214274 A214275 A214276

Keyword

nonn

Author

Alois P. Heinz, Jul 09 2012

Status

approved