OFFSET
0,2
REFERENCES
Stanley, Richard P., Linear homogeneous Diophantine equations and magic labelings of graphs. Duke Math. J. 40 (1973), 607-632.
Stanley, Richard P., Magic labelings of graphs, symmetric magic squares, systems of parameters, and Cohen-Macaulay rings. Duke Math. J. 43 (1976), no. 3, 511-531.
LINKS
Robert Israel, Table of n, a(n) for n = 0..10000
R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]
FORMULA
G.f.: (1+24*x+156*x^2+280*x^3+156*x^4+24*x^5+x^6)/(1-x)^10.
a(k) = 1+(25/6)*k+(3337/420)*k^2+(13777/1512)*k^3+(3289/480)*k^4+(9983/2880)*k^5+(281/240)*k^6+(73/288)*k^7+(107/3360)*k^8+(107/60480)*k^9. - Robert Israel, Jul 06 2014
EXAMPLE
a(1)=34:
0 1's: 1,
1 1: 9,
2 1's: 3*3*2 = 18,
3 1's: 6 (transversals),
total = 34.
MAPLE
f:= k -> 1+(25/6)*k+(3337/420)*k^2+(13777/1512)*k^3+(3289/480)*k^4+(9983/2880)*k^5+(281/240)*k^6+(73/288)*k^7+(107/3360)*k^8+(107/60480)*k^9:
seq(f(k), k=0..1000); # Robert Israel, Jul 06 2014
MATHEMATICA
CoefficientList[Series[(1 + 24*x + 156*x^2 + 280*x^3 + 156*x^4 + 24*x^5 + x^6)/(1 - x)^10, {x, 0, 30}], x] (* Wesley Ivan Hurt, Jul 06 2014 *)
PROG
(Magma) [1+(25/6)*k+(3337/420)*k^2+(13777/1512)*k^3+(3289/480)*k^4+(9983/2880)*k^5+(281/240)*k^6+(73/288)*k^7+(107/3360)*k^8+(107/60480)*k^9 : k in [0..30]]; // Wesley Ivan Hurt, Jul 06 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jul 06 2014
STATUS
approved