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A292350 Number of Lyndon words (aperiodic necklaces) with 6 beads of n colors. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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).

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)

PROG

(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

CROSSREFS

Row n=6 of A074650.

Sequence in context: A157570 A223499 A157233 * A188976 A180913 A083305

Adjacent sequences:  A292347 A292348 A292349 * A292351 A292352 A292353

KEYWORD

nonn,easy

AUTHOR

Eric M. Schmidt, Dec 08 2017

STATUS

approved

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Last modified August 9 22:42 EDT 2020. Contains 336335 sequences. (Running on oeis4.)