A107511 Coordination sequence for D_16 lattice

1, 480, 43072, 1535392, 30171264, 386224480, 3568285888, 25502776608, 148192248064, 726504898784, 3090942003520, 11666428964000, 39751306125696, 123999066493024, 358175327721920, 967087327771680, 2459947867603456, 5933762681602016, 13648859698457152

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Index entries for linear recurrences with constant coefficients, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).

Formula

G.f.: (x^16 + 464*x^15 + 35512*x^14 + 903280*x^13 + 10506652*x^12 + 64480208*x^11 + 225728776*x^10 + 471339504*x^9 + 600970566*x^8 + 471339504*x^7 + 225728776*x^6 + 64480208*x^5 + 10506652*x^4 + 903280*x^3 + 35512*x^2 + 464*x + 1) / (x - 1)^16. [Colin Barker, Nov 21 2012]

Mathematica

CoefficientList[Series[(x^16+464x^15+35512x^14+903280x^13+10506652x^12+64480208x^11+ 225728776x^10+471339504x^9+600970566x^8+471339504x^7+225728776x^6+64480208x^5+10506652x^4+903280x^3+35512x^2+464x+1)/(x-1)^16, {x, 0, 30}], x] (* or *) LinearRecurrence[ {16, -120, 560, -1820, 4368, -8008, 11440, -12870, 11440, -8008, 4368, -1820, 560, -120, 16, -1}, {1, 480, 43072, 1535392, 30171264, 386224480, 3568285888, 25502776608, 148192248064, 726504898784, 3090942003520, 11666428964000, 39751306125696, 123999066493024, 358175327721920, 967087327771680, 2459947867603456}, 30] (* Harvey P. Dale, Oct 14 2023 *)

Crossrefs

Sequence in context: A331768 A035314 A022047 * A288471 A008410 A305569

Adjacent sequences: A107508 A107509 A107510 * A107512 A107513 A107514

Keyword

nonn,easy

Author

N. J. A. Sloane, May 28 2005

Status

approved