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A008532 Coordination sequence for 4-dimensional I-centered cubic orthogonal lattice. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 5 12:34 EDT 2020. Contains 333241 sequences. (Running on oeis4.)