A244805 The 240-degree spoke (or ray) of a hexagonal spiral of Ulam.

1, 16, 55, 118, 205, 316, 451, 610, 793, 1000, 1231, 1486, 1765, 2068, 2395, 2746, 3121, 3520, 3943, 4390, 4861, 5356, 5875, 6418, 6985, 7576, 8191, 8830, 9493, 10180, 10891, 11626, 12385, 13168, 13975, 14806, 15661, 16540, 17443, 18370, 19321, 20296, 21295, 22318, 23365, 24436, 25531

Offset: 1

Author

Robert G. Wilson v, Jul 06 2014

Keywords

• nonn
• easy

Comments

Numbers of the form 1 + k/2 + k^2/3 (associated k are in A008588). - Bruno Berselli, Jan 20 2017

Examples

			See A056105 example section for its 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, A244802, A056106, A244803, A056107, A244804, A056108, A056109, A244806, A003215, A033577.

Cf. A281333 (1 + floor(n/2) + floor(n^2/3)).

Programs

Magma

[12*n^2-21*n+10: n in [1..50]]; // Wesley Ivan Hurt, Jul 06 2014

Maple

A244805:=n->12*n^2 - 21*n + 10: seq(A244805(n), n=1..50); # Wesley Ivan Hurt, Jul 06 2014

Mathematica

f[n_] := 12 n^2 - 21 n + 10; Array[f, 47]

PARI

vector(50, n, 12*n^2 - 21*n + 10) \\ Michel Marcus, Jul 06 2014

PARI

Vec(x*(1 + 13*x + 10*x^2) / (1 - x)^3 + O(x^50)) \\ Colin Barker, Dec 12 2016

Formula

a(n) = 12*n^2 - 21*n + 10 (see A056105).

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 + 13*x + 10*x^2) / (1 - x)^3.

(End)