|
| |
|
|
A016061
|
|
n*(n+1)*(4*n+5)/6.
|
|
10
| |
|
|
0, 3, 13, 34, 70, 125, 203, 308, 444, 615, 825, 1078, 1378, 1729, 2135, 2600, 3128, 3723, 4389, 5130, 5950, 6853, 7843, 8924, 10100, 11375, 12753, 14238, 15834, 17545, 19375, 21328, 23408, 25619, 27965, 30450, 33078, 35853, 38779, 41860
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| Number of ZnS molecules in cluster of n layers in zinc blend crystal.
The Kn4 triangle sums of the Connell-Pol triangle A159797 lead to the sequence given above. For the definitions of the Kn4 and other triangle sums see A180662. [From Johannes W. Meijer, May 20 2011]
If one generated primtive Pythagorean triangles (2n+1, 2n+3) the collective sum of their perimeters for each n is four times the numbers listed in this sequence. [From J. M. Bergot, Jul 18 2011]
|
|
|
REFERENCES
| T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, see p. 233.
G. Olive, Problem #504, Factorizations and Sums, Two-Year College Math. Jnl., 25 (1994), 244-245.
|
|
|
FORMULA
| G.f.: x*(3+x)/(1-x)^4 - Paul Barry (pbarry(AT)wit.ie), Feb 27 2003
Partial sums of n even-indexed triangular numbers, e.g. a(3)=t(0)+t(2)+t(4)=0+3+10=13 - Jon Perry (perry(AT)globalnet.co.uk), Jul 23 2003
a(n) = sum(i=0, n-1, 2*i^2 + i) - Jani Nurminen (slinky(AT)iki.fi), May 14 2006
|
|
|
MAPLE
| seq(add((n^2-k^2), k=1..n), n=1..40); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 01 2006
|
|
|
MATHEMATICA
| f[n_]:=4*n+3; s1=s2=0; lst={}; Do[a=f[n]; s1+=a; s2+=s1; AppendTo[lst, s2], {n, 0, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 25 2009]
|
|
|
PROG
| (PARI) v=vector(40, i, t(i)); s=0; forstep(i=2, 40, 2, s+=v[i]; print1(s", "))
|
|
|
CROSSREFS
| Bisection of A002623.
Cf. A002412.
Row sums of triangle A120070.
Sequence in context: A166805 A033943 A026084 * A154154 A137976 A095661
Adjacent sequences: A016058 A016059 A016060 * A016062 A016063 A016064
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com)
|
| |
|
|
