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

Author

Alois P. Heinz, Jul 09 2012

Keywords

• nonn

Examples

			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].
		

Links

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

Crossrefs

Column k=4 of A214269.

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