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

0,2

Comments

Let f(x) = x^2 + x + 1 then sequence gives f(f(n+1)) - f(f(n)), n >= 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).

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

Maple

1, seq( 4*k^3+6*k, k=1..40);

Mathematica

Table[If[n==0, 1, 2*n*(3+2*n^2)], {n, 0, 40}] (* G. C. Greubel, Nov 10 2019 *)

Prog

(PARI) Vec((x+1)^2*(x^2+4*x+1)/(x-1)^4 + O(x^40)) \\ Colin Barker, Mar 03 2015
(PARI) vector(46, n, if(n==1, 1, 2*(n-1)*(3 +2*(n-1)^2) ) ) \\ G. C. Greubel, Nov 10 2019
(Magma) [1] cat [2*n*(3+2*n^2): n in [1..45]]; // G. C. Greubel, Nov 10 2019
(Sage) [1]+[2*n*(3+2*n^2) for n in (1..45)]; # G. C. Greubel, Nov 10 2019
(GAP) Concatenation([1], List([1..45], n-> 2*n*(3+2*n^2) )); # G. C. Greubel, Nov 10 2019

Crossrefs

Sequence in context: A126964 A256050 A257052 * A085582 A058310 A005720

Adjacent sequences: A008529 A008530 A008531 * A008533 A008534 A008535

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved