OFFSET
5,2
LINKS
Colin Barker, Table of n, a(n) for n = 5..1000
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
FORMULA
a(n) = Sum_{k=0..5} binomial(n-k, 10-2*k). - Len Smiley, Oct 20 2001
a(n) = 34 -9161*n/280 -101897*n^3/20160 +794293*n^2/50400 -287*n^5/1280 +438209*n^4/362880 +5593*n^6/172800 -47*n^7/13440 -n^9/80640 +n^8/3780 +n^10/3628800. - R. J. Mathar, Oct 05 2009
G.f.: x^5*(1-x+x^2)*(1-5*x+9*x^2-5*x^3+x^4)*(1-3*x+5*x^2-3*x^3+x^4) / (1-x)^11. - Colin Barker, Feb 17 2016
MAPLE
seq(add(binomial(n-k, 10-2*k), k=0..5), n=5..40); # G. C. Greubel, Sep 27 2019
MATHEMATICA
Table[Sum[Binomial[n-k, 10-2k], {k, 0, 5}], {n, 5, 40}] (* or *)
Drop[#, 5] &@ CoefficientList[Series[x^5(1-x+x^2)(1-5x+9x^2-5x^3+x^4)(1- 3x+5x^2-3x^3+x^4)/(1-x)^11, {x, 0, 37}], x] (* Michael De Vlieger, Feb 17 2016 *)
PROG
(PARI) Vec(x^5*(1-x+x^2)*(1-5*x+9*x^2-5*x^3+x^4)*(1-3*x+5*x^2-3*x^3+x^4) / (1-x)^11 + O(x^40)) \\ Colin Barker, Feb 17 2016
(PARI) vector(40, n, sum(k=0, 5, binomial(n+4-k, 10-2*k)) ) \\ G. C. Greubel, Sep 27 2019
(Magma) [&+[Binomial(n-k, 10-2*k): k in [0..5]] : n in [5..40]]; // G. C. Greubel, Sep 27 2019
(Sage) [sum(binomial(n-k, 10-2*k) for k in (0..5)) for n in (5..40)] # G. C. Greubel, Sep 27 2019
(GAP) List([5..40], n-> Sum([0..5], k-> Binomial(n-k, 10-2*k)) ); # G. C. Greubel, Sep 27 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved