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A056105 First spoke of a hexagonal spiral. 15
1, 2, 9, 22, 41, 66, 97, 134, 177, 226, 281, 342, 409, 482, 561, 646, 737, 834, 937, 1046, 1161, 1282, 1409, 1542, 1681, 1826, 1977, 2134, 2297, 2466, 2641, 2822, 3009, 3202, 3401, 3606, 3817, 4034, 4257, 4486, 4721, 4962, 5209, 5462, 5721, 5986, 6257 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..46.

H. Bottomley, Illustration of initial terms

G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2

Index entries for sequences related to linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(n) = 3n^2-2n+1 = a(n-1)+6n-5 = 2a(n-1)-a(n-2)+6 = 3a(n-1)-3a(n-2)+a(n-3) = A056106(n)-n = A056107(n)-2n = A056108(n)-3n = A056109(n)-4n = A003215(n)-5n

a(n)=6*n+a(n-1)-5 (with a(0)=1) [From Vincenzo Librandi, Aug 07 2010]

G.f.: (1-x+6*x^2)/(1-3*x+3*x^2-x^3). [Colin Barker, Jan 04 2012]

EXAMPLE

a(1)=6*1+1-5=2; a(2)=6*2+2-5=9; a(3)=6*3+9-5=22 [From Vincenzo Librandi, Aug 07 2010]

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {1, 2, 9}, 50] (* Harvey P. Dale, Nov 02 2011 *)

PROG

(PARI) a(n)=3*n^2-2*n+1 /* Michael Somos Aug 03 2006 */

CROSSREFS

Cf. A054552 for example of square (or octagonal) spiral spoke.

A008810(3n-1)=A056109(-n)=a(n). - Michael Somos Aug 03 2006.

Sequence in context: A024850 A237044 A235707 * A212069 A106058 A086718

Adjacent sequences:  A056102 A056103 A056104 * A056106 A056107 A056108

KEYWORD

easy,nonn

AUTHOR

Henry Bottomley, Jun 09 2000

STATUS

approved

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Last modified April 24 12:03 EDT 2014. Contains 240983 sequences.