A244804 The 300-degree spoke (or ray) of a hexagonal spiral of Ulam.

1, 14, 51, 112, 197, 306, 439, 596, 777, 982, 1211, 1464, 1741, 2042, 2367, 2716, 3089, 3486, 3907, 4352, 4821, 5314, 5831, 6372, 6937, 7526, 8139, 8776, 9437, 10122, 10831, 11564, 12321, 13102, 13907, 14736, 15589, 16466, 17367, 18292, 19241, 20214, 21211, 22232, 23277, 24346, 25439

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..1000

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

Formula

See A056105 example section for its formula.

From Colin Barker, Dec 12 2016: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.

G.f.: x*(1 + 11*x + 12*x^2) / (1 - x)^3.

(End)

Example

See A056105 example section for its diagram.

Maple

A244804:=n->12*n^2 - 23*n + 12: seq(A244804(n), n=1..50); # Wesley Ivan Hurt, Jul 06 2014

Mathematica

f[n_] := 12n^2 - 23n + 12; Array[f, 47]

Prog

(PARI) vector(50, n, 12*n^2 - 23*n + 12) \\ Michel Marcus, Jul 06 2014
(PARI) Vec(x*(1 + 11*x + 12*x^2) / (1 - x)^3 + O(x^50)) \\ Colin Barker, Dec 12 2016
(Magma) [ 12*n^2 - 23*n + 12 : n in [1..50] ]; // Wesley Ivan Hurt, Jul 06 2014

Crossrefs

Cf. A056105, A244802, A056106, A244803, A056107, A056108, A244805, A056109, A244806, A003215, A033577.

Sequence in context: A043132 A039309 A043912 * A009961 A059997 A007588

Adjacent sequences: A244801 A244802 A244803 * A244805 A244806 A244807

Keyword

nonn,easy

Author

Robert G. Wilson v, Jul 06 2014

Status

approved