

A195147


Concentric 18gonal numbers.


13



0, 1, 18, 37, 72, 109, 162, 217, 288, 361, 450, 541, 648, 757, 882, 1009, 1152, 1297, 1458, 1621, 1800, 1981, 2178, 2377, 2592, 2809, 3042, 3277, 3528, 3781, 4050, 4321, 4608, 4897, 5202, 5509, 5832, 6157, 6498, 6841, 7200, 7561, 7938, 8317, 8712, 9109
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OFFSET

0,3


COMMENTS

Also concentric octadecagonal numbers or concentric octakaidecagonal numbers. Also sequence found by reading the line from 0, in the direction 0, 18, ..., and the same line from 1, in the direction 1, 37, ..., in the square spiral whose vertices are the generalized hendecagonal numbers A195160. Main axis, perpendicular to A027468 in the same spiral.


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (2,0,2,1).


FORMULA

G.f.: x*(1+16*x+x^2) / ( (1+x)*(x1)^3 ).  R. J. Mathar, Sep 18 2011
From Vincenzo Librandi, Sep 27 2011: (Start)
a(n) = (18*n^2 + 7*(1)^n  7)/4;
a(n) = a(n1) + 9*n^2  9*n + 1. (End)


PROG

(MAGMA) [(18*n^2+7*(1)^n7)/4: n in [0..50]]; // Vincenzo Librandi, Sep 27 2011
(PARI) a(n)=(18*n^2+7*(1)^n7)/4 \\ Charles R Greathouse IV, Sep 28 2015


CROSSREFS

Cf. A195321 and A195316 interleaved.
Cf. A032528, A077221, A195142, A195143, A195145, A195146, A195148, A195149.
Cf. A032527, A195047, A195048. Column 18 of A195040.  Omar E. Pol, Sep 29 2011
Sequence in context: A041638 A041636 A212428 * A198276 A041640 A041642
Adjacent sequences: A195144 A195145 A195146 * A195148 A195149 A195150


KEYWORD

nonn,easy


AUTHOR

Omar E. Pol, Sep 17 2011


STATUS

approved



