A292350 Number of Lyndon words (aperiodic necklaces) with 6 beads of n colors.

0, 9, 116, 670, 2580, 7735, 19544, 43596, 88440, 166485, 295020, 497354, 804076, 1254435, 1897840, 2795480, 4022064, 5667681, 7839780, 10665270, 14292740, 18894799, 24670536, 31848100, 40687400, 51482925, 64566684, 80311266, 99133020, 121495355, 147912160

Offset: 1

Author

Eric M. Schmidt, Dec 08 2017

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).

Crossrefs

Row n=6 of A074650.

Programs

PARI

concat(0, Vec(x^2*(9 + 53*x + 47*x^2 + 11*x^3) / (1 - x)^7 + O(x^40))) \\ Colin Barker, Dec 08 2017

Formula

a(n) = (n^6 - n^3 - n^2 + n)/6.

From Colin Barker, Dec 08 2017: (Start)

G.f.: x^2*(9 + 53*x + 47*x^2 + 11*x^3) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)