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A027930 a(n) = T(n, 2*n-7), T given by A027926. 2
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 (list; graph; refs; listen; history; text; internal format)
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

Cf. A228074.

Sequence in context: A267946 A166287 A186812 * A038200 A291039 A030015

Adjacent sequences:  A027927 A027928 A027929 * A027931 A027932 A027933

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified October 19 16:17 EDT 2019. Contains 328223 sequences. (Running on oeis4.)