A008532 Coordination sequence for 4-dimensional I-centered cubic orthogonal lattice.
1, 10, 44, 126, 280, 530, 900, 1414, 2096, 2970, 4060, 5390, 6984, 8866, 11060, 13590, 16480, 19754, 23436, 27550, 32120, 37170, 42724, 48806, 55440, 62650, 70460, 78894, 87976, 97730, 108180, 119350, 131264, 143946, 157420, 171710, 186840, 202834, 219716, 237510
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.
- M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908. [Annotated scanned copy]
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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GAP
Concatenation([1], List([1..45], n-> 2*n*(3+2*n^2) )); # G. C. Greubel, Nov 10 2019
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Magma
[1] cat [2*n*(3+2*n^2): n in [1..45]]; // G. C. Greubel, Nov 10 2019
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Maple
1, seq( 4*k^3+6*k, k=1..40);
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Mathematica
Table[If[n==0,1,2*n*(3+2*n^2)], {n,0,40}] (* G. C. Greubel, Nov 10 2019 *) -
PARI
Vec((x+1)^2*(x^2+4*x+1)/(x-1)^4 + O(x^40)) \\ Colin Barker, Mar 03 2015
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PARI
vector(46, n, if(n==1,1, 2*(n-1)*(3 +2*(n-1)^2) ) ) \\ G. C. Greubel, Nov 10 2019
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Sage
[1]+[2*n*(3+2*n^2) for n in (1..45)]; # G. C. Greubel, Nov 10 2019
Formula
a(n) = 4*n^3 + 6*n, n >= 1.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4. - Colin Barker, Mar 03 2015
G.f.: (1+x)^2*(1+4*x+x^2)/(1-x)^4. - Colin Barker, Mar 03 2015
a(0) = 1; for n > 0, a(n) = A005898(n-1) + A005898(n) = (n-1)^3 + 2n^3 + (n+1)^3. - Doug Bell, Aug 18 2015
E.g.f.: 1 + 2*x*(5 + 6*x + 2*x^2)*exp(x). - G. C. Greubel, Aug 21 2015
Comments