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A008527
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Coordination sequence for body-centered tetragonal lattice.
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34
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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, 10370, 10954, 11554, 12170, 12802, 13450, 14114, 14794, 15490, 16202, 16930, 17674
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OFFSET
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0,2
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COMMENTS
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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
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LINKS
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FORMULA
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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, ...]. (End)
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. (End)
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MAPLE
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1, seq(8*k^2+2, k=1..50);
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MATHEMATICA
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a[0]:= 1; a[n_]:= 8n^2 +2; Table[a[n], {n, 0, 50}] (* Alonso del Arte, Sep 06 2011 *)
LinearRecurrence[{3, -3, 1}, {1, 10, 34, 74}, 50] (* Harvey P. Dale, Feb 13 2022 *)
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PROG
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(PARI) vector(51, n, if(n==1, 1, 2*(1+(2*n-2)^2)) ) \\ G. C. Greubel, Nov 09 2019
(Magma) [1] cat [2*(1 + 4*n^2): n in [1..50]]; // G. C. Greubel, Nov 09 2019
(Sage) [1]+[2*(1+4*n^2) for n in (1..40)] # G. C. Greubel, Nov 09 2019
(GAP) Concatenation([1], List([1..40], n-> 2*(1+4*n^2) )); # G. C. Greubel, Nov 09 2019
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CROSSREFS
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Apart from leading term, same as A108100.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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