A027930 a(n) = T(n, 2*n-7), T given by A027926.

1, 3, 8, 21, 54, 133, 309, 674, 1383, 2683, 4950, 8735, 14820, 24285, 38587, 59652, 89981, 132771, 192052, 272841, 381314, 524997, 712977, 956134, 1267395, 1662011, 2157858, 2775763, 3539856, 4477949, 5621943, 7008264, 8678329, 10679043, 13063328, 15890685

Offset: 4

Author

Clark Kimberling

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A228074.

Programs

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

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

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 *)

PARI

vector(40, n, binomial(n+3, n-4) + n*(n^4 +15*n^2 +104)/120) \\ 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

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)