|
|
A244805
|
|
The 240-degree spoke (or ray) of a hexagonal spiral of Ulam.
|
|
8
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 12*n^2 - 21*n + 10 (see A056105).
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)
|
|
EXAMPLE
|
See A056105 example section for its diagram.
|
|
MAPLE
|
|
|
MATHEMATICA
|
f[n_] := 12 n^2 - 21 n + 10; Array[f, 47]
|
|
PROG
|
(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
|
|
CROSSREFS
|
Cf. A056105, A244802, A056106, A244803, A056107, A244804, A056108, A056109, A244806, A003215, A033577.
Cf. A281333 (1 + floor(n/2) + floor(n^2/3)).
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|