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

Author

Robert G. Wilson v, Jul 06 2014

Keywords

• nonn
• easy

Examples

			See A056105 example section for a diagram.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

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

Programs

Magma

[12*n^2-27*n+16 : n in [1..50]]; // Wesley Ivan Hurt, Jul 06 2014

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]

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

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)