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A321416 Number of n element multisets of the 10th roots of unity with zero sum. 2
1, 0, 5, 0, 15, 2, 35, 10, 70, 30, 128, 70, 220, 140, 360, 254, 565, 430, 855, 690, 1255, 1060, 1795, 1570, 2510, 2256, 3440, 3160, 4630, 4330, 6132, 5820, 8005, 7690, 10315, 10008, 13135, 12850, 16545, 16300, 20634, 20450, 25500, 25400, 31250, 31260 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Equivalently, the number of closed convex paths of length n whose steps are the 10th roots of unity up to translation. For even n, there will be 5 paths of zero area consisting of n/2 steps in one direction followed by n/2 steps in the opposite direction.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,4,-4,-6,7,3,-8,3,7,-6,-4,4,1,-1)

FORMULA

G.f.: (1 - x^10)/((1 - x^2)^5 * (1 - x^5)^2).

G.f.: (1 - x + x^2 - x^3 + x^4)/((1 + x + x^2 + x^3 + x^4)*(1 - x)^6*(1 + x)^4).

MATHEMATICA

LinearRecurrence[{1, 4, -4, -6, 7, 3, -8, 3, 7, -6, -4, 4, 1, -1}, {1, 0, 5, 0, 15, 2, 35, 10, 70, 30, 128, 70, 220, 140}, 50] (* Jinyuan Wang, Feb 28 2020 *)

PROG

(PARI) Vec((1 - x^10)/((1 - x^2)^5 * (1 - x^5)^2) + O(x^50))

CROSSREFS

Column k=5 of A321414.

Cf. A053090, A070190.

Sequence in context: A290867 A027635 A291218 * A226372 A093782 A085105

Adjacent sequences:  A321413 A321414 A321415 * A321417 A321418 A321419

KEYWORD

nonn,easy

AUTHOR

Andrew Howroyd, Nov 09 2018

STATUS

approved

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Last modified March 6 03:33 EST 2021. Contains 341840 sequences. (Running on oeis4.)