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A354343

Number of distinct sums of n complex 6th power roots of unity.

1, 6, 19, 37, 61, 91, 127, 169, 217, 271, 331, 397, 469, 547, 631, 721, 817, 919, 1027, 1141, 1261, 1387, 1519, 1657, 1801, 1951, 2107, 2269, 2437, 2611, 2791, 2977, 3169, 3367, 3571, 3781, 3997, 4219, 4447, 4681, 4921, 5167, 5419, 5677, 5941, 6211, 6487, 6769, 7057, 7351, 7651, 7957

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..51.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

For n >= 2, a(n) = 3*n^2 + 3*n + 1 = A003215(n).

For n >= 5, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

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

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {1, 6, 19, 37, 61}, 60] (* Harvey P. Dale, Nov 03 2024 *)