A244803 The 360 degree spoke (or ray) of a hexagonal spiral of Ulam.

1, 12, 47, 106, 189, 296, 427, 582, 761, 964, 1191, 1442, 1717, 2016, 2339, 2686, 3057, 3452, 3871, 4314, 4781, 5272, 5787, 6326, 6889, 7476, 8087, 8722, 9381, 10064, 10771, 11502, 12257, 13036, 13839, 14666, 15517, 16392, 17291, 18214, 19161, 20132, 21127, 22146, 23189, 24256, 25347

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

(End)

Example

See A056105 example section for a diagram.

Maple

A244803:=n->12*n^2-25*n+14: seq(A244803(n), n=1..50); # Wesley Ivan Hurt, Jul 06 2014

Mathematica

f[n_] := 12n^2 - 25n + 14; Array[f, 47]

Prog

(PARI) vector(50, n, 12*n^2 - 25*n + 14) \\ Michel Marcus, Jul 06 2014
(PARI) Vec(x*(1 + 2*x)*((1 + 7*x) / (1 - x)^3) + O(x^50)) \\ Colin Barker, Dec 12 2016
(Magma) [12*n^2-25*n+14 : n in [1..50]]; // Wesley Ivan Hurt, Jul 06 2014

Crossrefs

Cf. A056105, A244802, A056106, A056107, A244804, A056108, A244805, A056109, A244806, A003215, A033577.

Sequence in context: A197471 A159013 A022281 * A024183 A051673 A030623

Adjacent sequences: A244800 A244801 A244802 * A244804 A244805 A244806

Keyword

nonn,easy

Author

Robert G. Wilson v, Jul 06 2014

Status

approved