OFFSET
0,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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).
Xiaogang Liang, Ilyar Hamid, and Haiming Duan, Dynamic stabilities of icosahedral-like clusters and their ability to form quasicrystals, AIP Advances 6, 065017 (2016).
Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).
FORMULA
Nearest integer to (7/8)*( (n+1)^4 - n^4 ).
G.f.: (x^4+10*x^3+20*x^2+10*x+1)/(x-1)^4/(x+1).
a(n) = 7*(2*n+1)*(2*n^2+2*n+1)/8 +(-1)^n/8. - R. J. Mathar, Mar 24 2011
a(0)=1, a(1)=13, a(2)=57, a(3)=153, a(4)=323, a(n)=3*a(n-1)- 2*a(n-2)- 2*a(n-3)+3*a(n-4)-a(n-5). - Harvey P. Dale, Jul 15 2011
E.g.f.: ((4 + 49*x + 63*x^2 + 14*x^3)*cosh(x) + (3 + 49*x + 63*x^2+ 14*x^3)*sinh(x))/4. - Stefano Spezia, Mar 14 2024
MATHEMATICA
Table[Floor[(7((n+1)^4-n^4)+4)/8], {n, 0, 40}] (* or *) LinearRecurrence[ {3, -2, -2, 3, -1}, {1, 13, 57, 153, 323}, 40] (* Harvey P. Dale, Jul 15 2011 *)
PROG
(PARI) j=[]; for(n=0, 75, j=concat(j, round((7/8)*((n+1)^4-n^4)))); j
(Python)
def a(n): return round((7/8)*((n+1)**4-n**4))
print([a(n) for n in range(36)]) # Michael S. Branicky, Jan 13 2021
CROSSREFS
Partial sums of A007899.
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.
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
More terms from Jason Earls, Jul 14 2001
STATUS
approved