A027929 a(n) = T(n, 2*n-6), T given by A027926.

1, 2, 5, 13, 33, 79, 176, 365, 709, 1300, 2267, 3785, 6085, 9465, 14302, 21065, 30329, 42790, 59281, 80789, 108473, 143683, 187980, 243157, 311261, 394616, 495847, 617905, 764093, 938093, 1143994, 1386321, 1670065, 2000714

Offset

3,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 3..1000

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

a(n) = Sum_{k=0..3} binomial(n-k, 6-2*k). - Len Smiley, Oct 20 2001

From Colin Barker, May 01 2012: (Start)

a(n) = (3600 -3420*n +1684*n^2 -525*n^3 +115*n^4 -15*n^5 +n^6)/720.

G.f.: x^3*(1-x+x^2)*(1-4*x+7*x^2-4*x^3+x^4)/(1-x)^7. (End)

E.g.f.: (3600 - 2160*x + 720*x^2 - 120*x^3 + 30*x^4 + x^6)*exp(x)/720 - 5 + 2*x - x^2/2. - G. C. Greubel, Sep 06 2019

Maple

seq((3600 -3420*n +1684*n^2 -525*n^3 +115*n^4 -15*n^5 +n^6)/720, n=3..40); # G. C. Greubel, Sep 06 2019

Mathematica

CoefficientList[Series[(1-x+x^2)(1-4x+7x^2-4x^3+x^4)/(1-x)^7, {x, 0, 40}], x] (* Vincenzo Librandi, Oct 18 2013 *)

Prog

(PARI) vector(40, n, m=n+2; (3600 -3420*m +1684*m^2 -525*m^3 +115*m^4 -15*m^5 +m^6)/720) \\ G. C. Greubel, Sep 06 2019
(Magma) [(3600 -3420*n +1684*n^2 -525*n^3 +115*n^4 -15*n^5 +n^6)/720: n in [3..40]]; // G. C. Greubel, Sep 06 2019
(Sage) [(3600 -3420*n +1684*n^2 -525*n^3 +115*n^4 -15*n^5 +n^6)/720 for n in (3..40)] # G. C. Greubel, Sep 06 2019
(GAP) List([3..40], n-> (3600 -3420*n +1684*n^2 -525*n^3 +115*n^4 -15*n^5 +n^6)/720); G. C. Greubel, Sep 06 2019

Crossrefs

Cf. A228074.

Sequence in context: A220739 A337282 A366117 * A001659 A088921 A005183

Adjacent sequences: A027926 A027927 A027928 * A027930 A027931 A027932

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved