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

Offset: 0

Author

Max Alekseyev, Aug 15 2022

Keywords

• nonn
• easy

Links

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

Crossrefs

Same as A003215 except for a(1) = 6.

Row 6 of A299807.

Cf. A000012, A000027, A000217, A000290, A000332, A000579, A014820, A103314, A107754, A107861, A108380, A107848, A107753, A108381, A143008, A299754.

Programs

Mathematica

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

PARI

a(n)=if(n==1, 6, 3*n*(n+1)+1) \\ Charles R Greathouse IV, Aug 15 2022

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.