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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
OFFSET
1,2
COMMENTS
Numbers of the form 1 + k/2 + k^2/3 (associated k are in A008588). - Bruno Berselli, Jan 20 2017
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)
EXAMPLE
See A056105 example section for its diagram.
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]
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
(Magma) [12*n^2-21*n+10: n in [1..50]]; // Wesley Ivan Hurt, Jul 06 2014
CROSSREFS
Cf. A281333 (1 + floor(n/2) + floor(n^2/3)).
Sequence in context: A172190 A122658 A224040 * A362039 A188838 A256049
KEYWORD
nonn,easy
AUTHOR
Robert G. Wilson v, Jul 06 2014
STATUS
approved