A063489 a(n) = (2*n-1)*(5*n^2-5*n+6)/6.

1, 8, 30, 77, 159, 286, 468, 715, 1037, 1444, 1946, 2553, 3275, 4122, 5104, 6231, 7513, 8960, 10582, 12389, 14391, 16598, 19020, 21667, 24549, 27676, 31058, 34705, 38627, 42834, 47336, 52143, 57265, 62712, 68494, 74621, 81103, 87950, 95172, 102779, 110781, 119188

Offset: 1

Author

N. J. A. Sloane, Aug 01 2001

Keywords

• nonn
• easy

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000
• T. P. Martin, Shells of atoms, Phys. Rep., 273 (1996), 199-241, eq. (10).
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

1/12*t*(2*n^3-3*n^2+n)+2*n-1 for t = 2, 4, 6, ... gives A049480, A005894, A063488, A001845, A063489, A005898, A063490, A057813, A063491, A005902, A063492, A005917, A063493, A063494, A063495, A063496.

Partial sums of A010001.

The 28 uniform 3D tilings: cab: A299266, A299267; crs: A299268, A299269; fcu: A005901, A005902; fee: A299259, A299265; flu-e: A299272, A299273; fst: A299258, A299264; hal: A299274, A299275; hcp: A007899, A007202; hex: A005897, A005898; kag: A299256, A299262; lta: A008137, A299276; pcu: A005899, A001845; pcu-i: A299277, A299278; reo: A299279, A299280; reo-e: A299281, A299282; rho: A008137, A299276; sod: A005893, A005894; sve: A299255, A299261; svh: A299283, A299284; svj: A299254, A299260; svk: A010001, A063489; tca: A299285, A299286; tcd: A299287, A299288; tfs: A005899, A001845; tsi: A299289, A299290; ttw: A299257, A299263; ubt: A299291, A299292; bnn: A007899, A007202. See the Proserpio link in A299266 for overview.

Programs

Magma

[(2*n-1)*(5*n^2-5*n+6)/6: n in [1..30]]; // G. C. Greubel, Dec 01 2017

Mathematica

Table[(2n-1)(5n^2-5n+6)/6,{n,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{1,8,30,77},40] (* Harvey P. Dale, Aug 20 2012 *)

PARI

a(n) = { (2*n - 1)*(5*n^2 - 5*n + 6)/6 } \\ Harry J. Smith, Aug 23 2009

PARI

my(x='x+O('x^30)); Vec(serlaplace((-6 + 12*x + 15*x^2 + 10*x^3 )*exp(x)/6 + 1)) \\ G. C. Greubel, Dec 01 2017

Formula

G.f.: x*(1+x)*(1+3*x+x^2)/(1-x)^4. - Colin Barker, Mar 02 2012

a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4), with a(1)=1, a(2)=8, a(3)=30, a(4)=77. - Harvey P. Dale, Aug 20 2012

E.g.f.: (-6 + 12*x + 15*x^2 + 10*x^3)*exp(x)/6 + 1. - G. C. Greubel, Dec 01 2017