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A214273 Number of compositions of n where the difference between largest and smallest parts equals 4 and adjacent parts are unequal. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 18 12:28 EDT 2020. Contains 337169 sequences. (Running on oeis4.)