A244802 The 60-degree spoke (or ray) of a hexagonal spiral of Ulam.

1, 10, 43, 100, 181, 286, 415, 568, 745, 946, 1171, 1420, 1693, 1990, 2311, 2656, 3025, 3418, 3835, 4276, 4741, 5230, 5743, 6280, 6841, 7426, 8035, 8668, 9325, 10006, 10711, 11440, 12193, 12970, 13771, 14596, 15445, 16318, 17215, 18136, 19081, 20050, 21043, 22060, 23101, 24166, 25255

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 a 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 + 7*x + 16*x^2) / (1 - x)^3.

(End)

Example

See A056105 example section for a diagram.

Maple

A244802:=n->12*n^2-27*n+16: seq(A244802(n), n=1..50); # Wesley Ivan Hurt, Jul 06 2014

Mathematica

f[n_] := 12n^2 - 27n + 16; Array[f, 47]

Prog

(PARI) vector(50, n, 12*n^2 - 27*n + 16) \\ Michel Marcus, Jul 06 2014
(PARI) Vec(x*(1 + 7*x + 16*x^2) / (1 - x)^3 + O(x^50)) \\ Colin Barker, Dec 12 2016
(Magma) [12*n^2-27*n+16 : n in [1..50]]; // Wesley Ivan Hurt, Jul 06 2014

Crossrefs

Cf. A056105, A056106, A244803, A056107, A244804, A056108, A244805, A056109, A244806, A003215.

Sequence in context: A084036 A092117 A245663 * A336288 A211070 A251936

Adjacent sequences: A244799 A244800 A244801 * A244803 A244804 A244805

Keyword

nonn,easy

Author

Robert G. Wilson v, Jul 06 2014

Status

approved