A008533 Coordination sequence for {A_5}* lattice.

1, 12, 72, 272, 762, 1752, 3512, 6372, 10722, 17012, 25752, 37512, 52922, 72672, 97512, 128252, 165762, 210972, 264872, 328512, 403002, 489512, 589272, 703572, 833762, 981252, 1147512, 1334072, 1542522, 1774512, 2031752, 2316012, 2629122, 2972972, 3349512

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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 (5,-10,10,-5,1).

Programs

GAP

Concatenation([1], List([1..45], n-> (4+15*n^2+5*n^4)/2 )); # G. C. Greubel, Nov 10 2019

Magma

[1] cat [(4+15*n^2+5*n^4)/2: n in [1..45]]; // G. C. Greubel, Nov 10 2019

Maple

1, seq( (5*k^4+15*k^2+4)/2, k=1..40);

Mathematica

Table[If[n==0, 1, (4+15*n^2+5*n^4)/2], {n,0,40}] (* G. C. Greubel, Nov 10 2019 *)
LinearRecurrence[{5,-10,10,-5,1},{1,12,72,272,762,1752},50] (* Harvey P. Dale, Jan 08 2020 *)

PARI

Vec(-(x+1)*(x^4+6*x^3+16*x^2+6*x+1) / (x-1)^5 + O(x^40)) \\ Colin Barker, Mar 03 2015

PARI

vector(46, n, if(n==1,1, (4 +15*(n-1)^2 +5*(n-1)^4)/2 ) ) \\ G. C. Greubel, Nov 10 2019

Sage

[1]+[(4+15*n^2+5*n^4)/2 for n in (1..45)]; # G. C. Greubel, Nov 10 2019

Formula

a(n) = 5*a(n-1) -10*a(n-2) +10*a(n-3) -5*a(n-4) +a(n-5) for n>5. - Colin Barker, Mar 03 2015

G.f.: (1+x)*(1+6*x+16*x^2+6*x^3+x^4)/(1-x)^5. - Colin Barker, Mar 03 2015

E.g.f.: -1 + (4 + 20*x + 50*x^2 + 30*x^3 + 5*x^4)*exp(x)/2. - G. C. Greubel, Nov 10 2019