A244806 The 180-degree spoke (or ray) of a hexagonal spiral of Ulam.

1, 18, 59, 124, 213, 326, 463, 624, 809, 1018, 1251, 1508, 1789, 2094, 2423, 2776, 3153, 3554, 3979, 4428, 4901, 5398, 5919, 6464, 7033, 7626, 8243, 8884, 9549, 10238, 10951, 11688, 12449, 13234, 14043, 14876, 15733, 16614, 17519, 18448, 19401, 20378, 21379, 22404, 23453, 24526, 25623

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

a(n) = 12*n^2 - 19*n + 8.

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 + 15*x + 8*x^2) / (1 - x)^3.

(End)

Example

See A056105 example section for its diagram.

Maple

A244806:=n->12*n^2 - 19*n + 8: seq(A244806(n), n=1..50); # Wesley Ivan Hurt, Jul 06 2014

Mathematica

f[n_] := 12n^2 - 19n + 8; Array[f, 47]

Prog

(PARI) vector(50, n, 12*n^2 - 19*n + 8) \\ Michel Marcus, Jul 06 2014
(PARI) Vec(x*(1 + 15*x + 8*x^2) / (1 - x)^3 + O(x^50)) \\ Colin Barker, Dec 12 2016
(Magma) [12*n^2 - 19*n + 8 : n in [1..50]]; // Wesley Ivan Hurt, Jul 06 2014

Crossrefs

Cf. A056105, A244802, A056106, A244803, A056107, A244804, A056108, A244805, A056109, A003215, A033577.

Sequence in context: A299460 A155155 A048356 * A027055 A056448 A056438

Adjacent sequences: A244803 A244804 A244805 * A244807 A244808 A244809

Keyword

nonn,easy

Author

Robert G. Wilson v, Jul 06 2014

Status

approved