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A244805 The 240º 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

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

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 - 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. A056105, A244802, A056106, A244803, A056107, A244804, A056108, A056109, A244806, A003215, A033577.

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

Sequence in context: A172190 A122658 A224040 * A188838 A256049 A152096

Adjacent sequences:  A244802 A244803 A244804 * A244806 A244807 A244808

KEYWORD

nonn,easy

AUTHOR

Robert G. Wilson v, Jul 06 2014

STATUS

approved

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Last modified December 13 19:20 EST 2017. Contains 295976 sequences.