A027933 a(n) = T(n, 2*n-10), T given by A027926.

1, 2, 5, 13, 34, 89, 232, 596, 1490, 3588, 8273, 18228, 38403, 77533, 150438, 281403, 509015, 892926, 1523117, 2532359, 4112704, 6536993, 10186540, 15586342, 23449376, 34731776, 50700937, 73018870, 103843433, 145950389, 202879594, 279108997, 380260541

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

Cf. A027926, A228074.

Sequence in context: A209230 A103142 A112844 * A141448 A011783 A001519

Adjacent sequences: A027930 A027931 A027932 * A027934 A027935 A027936

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved