OFFSET
4,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 4..1003
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
FORMULA
a(n) = Sum_{k=0..3} binomial(n-k, 7-2k). - Len Smiley, Oct 20 2001
a(n) = C(n-3,n-4)+C(n-2,n-5)+C(n-1,n-6)+C(n,n-7). - Zerinvary Lajos, May 29 2007
From R. J. Mathar, Oct 05 2009: (Start)
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8).
G.f.: x^4*(1 - x + x^2)*(1 - 4*x + 7*x^2 - 4*x^3 + x^4)/(1-x)^8. (End)
From G. C. Greubel, Sep 06 2019: (Start)
a(n) = binomial(n-1, n-7) + (n-3)*((n-3)^4 + 15*(n-3)^2 + 104)/120.
E.g.f.: x*(5040 + 2520*x + 1680*x^2 + 630*x^3 + 168*x^4 + 21*x^5 + x^6)*exp(x)/5040. (End)
MAPLE
seq(binomial(n-3, n-4)+binomial(n-2, n-5)+binomial(n-1, n-6)+binomial(n, n-7) , n=4..50); # Zerinvary Lajos, May 29 2007
MATHEMATICA
Table[Total[Binomial[First[#], Last[#]]&/@Table[{n+i, n-1-i}, {i, 0, 3}]], {n, 35}] (* or *) LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {1, 3, 8, 21, 54, 133, 309, 674}, 35] (* Harvey P. Dale, Jun 23 2011 *)
PROG
(PARI) vector(40, n, binomial(n+3, n-4) + n*(n^4 +15*n^2 +104)/120) \\ G. C. Greubel, Sep 06 2019
(Magma) [Binomial(n-1, n-7) + (n-3)*((n-3)^4 +15*(n-3)^2 +104)/120: n in [4..40]]; // G. C. Greubel, Sep 06 2019
(Sage) [binomial(n-1, n-7) + (n-3)*((n-3)^4 +15*(n-3)^2 +104)/120 for n in (4..40)] # G. C. Greubel, Sep 06 2019
(GAP) List([4..40], n-> Binomial(n-1, n-7) + (n-3)*((n-3)^4 +15*(n-3)^2 +104)/120); # G. C. Greubel, Sep 06 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved