

A008527


Coordination sequence for bodycentered tetragonal lattice.


19



1, 10, 34, 74, 130, 202, 290, 394, 514, 650, 802, 970, 1154, 1354, 1570, 1802, 2050, 2314, 2594, 2890, 3202, 3530, 3874, 4234, 4610, 5002, 5410, 5834, 6274, 6730, 7202, 7690, 8194, 8714, 9250, 9802
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OFFSET

0,2


COMMENTS

Also sequence found by reading the segment (1, 10) together with the line from 10, in the direction 10, 34,..., in the square spiral whose vertices are the generalized hexagonal numbers A000217.  Omar E. Pol, Nov 02 2012


REFERENCES

M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905908.


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905908. [Annotated scanned copy]


FORMULA

a(0) = 1; a(n) = 8*n^2+2 for n>0.
a(n) = (2n+1)^2 + (2n1)^2 for n>0. Binomial transform of [1, 9, 15, 1, 1, 1, 1, 1,...].  Gary W. Adamson, Dec 27 2007
a(n) = 3*a(n1)3*a(n2)+a(n3) for n>3. G.f.: (1+x)*(1+6*x+x^2)/(1x)^3. [Colin Barker, Apr 13 2012]


MAPLE

[ seq( 8*k^2+2, k=0..40) ];


MATHEMATICA

a[0] := 1; a[n_] := 8n^2 + 2; Table[a[n], {n, 0, 35}] (* Alonso del Arte, Sep 06 2011 *)


CROSSREFS

Apart from leading term, same as A108100.
Cf. A206399.
Sequence in context: A020495 A155486 A225276 * A007584 A218329 A009924
Adjacent sequences: A008524 A008525 A008526 * A008528 A008529 A008530


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane.


STATUS

approved



