OFFSET
1,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000
K. S. Brown, The Dartboard Sequence
H. L. Montgomery, Kevin Brown's enumeration problem, Manuscript, 4 Oct. 1994. (Annotated scanned copy)
FORMULA
For n >= 7, a(n) = (n^3-16*n+27)/6 (n odd); (n^3-16*n+30)/6 (n even).
G.f.: x*(1-2*x+4*x^3+3*x^5-10*x^7+2*x^8+8*x^9-4*x^10)/((1-x)^3*(1-x^2)). - Michael Somos, May 03, 2002
a(2n) = A322594(n-4), n>=4. - R. J. Mathar, Mar 18 2019
MATHEMATICA
Drop[CoefficientList[Series[x*(1-2*x+4*x^3+3*x^5-10*x^7+2*x^8+8*x^9 -4*x^10)/((1-x)^3*(1-x^2)), {x, 0, 60}], x], 1] (* G. C. Greubel, Mar 15 2019 *)
PROG
(PARI) a(n)=polcoeff(x*(1-2*x+4*x^3+3*x^5-10*x^7+2*x^8+8*x^9-4*x^10+O(x^n))/(1-x)^3/(1-x^2), n)
(PARI) A007773(n)=if(n>5, (n^3-max(16*n, 116)+31)\6, n>3, 5*n-17, 1) \\ M. F. Hasler, Mar 15 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( x*(1-2*x +4*x^3+3*x^5-10*x^7+2*x^8+8*x^9-4*x^10)/((1-x)^3*(1-x^2)) )); // G. C. Greubel, Mar 15 2019
(Sage) a=(x*(1-2*x+4*x^3+3*x^5-10*x^7+2*x^8+8*x^9-4*x^10)/((1-x)^3*(1-x^2))).series(x, 60).coefficients(x, sparse=False); a[1:] # G. C. Greubel, Mar 15 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
K. S. Brown (kevin2003(AT)delphi.com), Hugh L. Montgomery
EXTENSIONS
More terms from David W. Wilson, Oct 27 2000
STATUS
approved