|
| |
|
|
A056106
|
|
Second spoke of a hexagonal spiral.
|
|
11
| |
|
|
1, 3, 11, 25, 45, 71, 103, 141, 185, 235, 291, 353, 421, 495, 575, 661, 753, 851, 955, 1065, 1181, 1303, 1431, 1565, 1705, 1851, 2003, 2161, 2325, 2495, 2671, 2853, 3041, 3235, 3435, 3641, 3853, 4071, 4295, 4525, 4761, 5003, 5251, 5505, 5765, 6031, 6303
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
H. Bottomley, Spokes of a hexagonal spiral (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-n+1 = a(n-1)+6n-4 = 2a(n-1)-a(n-2)+6 = 3a(n-1)-3a(n-2)+a(n-3).
E.g.f.: (1+2*x+3*x^2)*exp(x). - Paul Barry, Mar 13 2003
a(n) = A096777(3*n) for n>0. - Reinhard Zumkeller, Dec 29 2007
G.f.: (1+5*x^2)/(1-3*x+3*x^2-x^3). [Colin Barker, Jan 04 2012]
|
|
|
MATHEMATICA
| s=1; lst={s}; Do[s+=n+1; AppendTo[lst, s], {n, 1, 6!, 6}]; lst [From Vladimir Orlovsky, Oct 25 2008]
|
|
|
PROG
| (MAGMA) I:=[1, 3]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2)+6: n in [1..50]]; // Vincenzo Librandi, Nov 14 2011
|
|
|
CROSSREFS
| Cf. A054552 for example of square (or octagonal) spiral spoke.
Sequence in context: A112051 A185258 A118436 * A147382 A184634 A164303
Adjacent sequences: A056103 A056104 A056105 * A056107 A056108 A056109
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Jun 09 2000
|
| |
|
|
