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A008527 Coordination sequence for body-centered 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 (list; graph; refs; listen; history; text; internal format)
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), 905-908.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908. [Annotated scanned copy]

FORMULA

a(0) = 1; a(n) = 8*n^2+2 for n>0.

a(n) = (2n+1)^2 + (2n-1)^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(n-1)-3*a(n-2)+a(n-3) for n>3. G.f.: (1+x)*(1+6*x+x^2)/(1-x)^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

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Last modified February 21 22:56 EST 2018. Contains 299427 sequences. (Running on oeis4.)