A010024 Coordination sequence for squashed {D_5}* lattice, perhaps the smallest example of a "non-superficial" lattice.

1, 12, 72, 292, 862, 2052, 4212, 7772, 13242, 21212, 32352, 47412, 67222, 92692, 124812, 164652, 213362, 272172, 342392, 425412, 522702, 635812, 766372, 916092, 1086762, 1280252, 1498512, 1743572, 2017542, 2322612, 2661052, 3035212, 3447522, 3900492, 4396712

Offset

0,2

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).

Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

Formula

a(n) = 10/3*n^4-5/3*n^3+20/3*n^2+5/3*n+2 for n>0 (from Maple section).

From Gopinath A. R., Feb 14 2012, (Start)

G.f.: -(x^5+7*x^4+42*x^3+22*x^2+7*x+1)/(x^5-5*x^4+10*x^3-10*x^2+5*x-1).

E.g.f.: 1/3*(10*x^4+55*x^3+75*x^2+30*x+6)*e^x-1. (End)

Maple

10/3*n^4-5/3*n^3+20/3*n^2+5/3*n+2;

Prog

(Magma) [1] cat [10/3*n^4-5/3*n^3+20/3*n^2+5/3*n+2: n in [1..40]]; // Vincenzo Librandi, Aug 03 2015

Crossrefs

Sequence in context: A300847 A235870 A008533 * A008414 A052181 A118979

Adjacent sequences: A010021 A010022 A010023 * A010025 A010026 A010027

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved