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A027818 a(n) = (n+1)*binomial(n+6,6). 5
1, 14, 84, 336, 1050, 2772, 6468, 13728, 27027, 50050, 88088, 148512, 241332, 379848, 581400, 868224, 1268421, 1817046, 2557324, 3542000, 4834830, 6512220, 8665020, 11400480, 14844375, 19143306, 24467184, 31011904 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) = A245334(n+6,6)/A000142(6). - Reinhard Zumkeller, Aug 31 2014

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

FORMULA

Number of 13-subsequences of [ 1, n ] with just 6 contiguous pairs; g.f.: (1+6x)/(1-x)^8.

a(n) = C(n+1, 1)*C(n+6, 6). - Zerinvary Lajos, May 26 2005

a(n) = n*(n-1)*(n-2)*(n-3)*(n-4)*(n-5)^2/6!, n=>6. - Zerinvary Lajos, Oct 19 2006

MAPLE

[seq(n*(n-1)*(n-2)*(n-3)*(n-4)*(n-5)^2/6!, n=6..33)]; # Zerinvary Lajos, Oct 19 2006

a:=n->sum((binomial(4, j)+binomial(n, 6)), j=6..n): seq(a(n), n=6..33); # Zerinvary Lajos, Feb 12 2007

MATHEMATICA

f[n_]:=7*n+1; s1=s2=s3=s4=s5=s6=0; lst={}; Do[a=f[n]; s1+=a; s2+=s1; s3+=s2; s4+=s3; s5+=s4; s6+=s5; AppendTo[lst, s6], {n, 0, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jun 25 2009 *)

PROG

(Haskell)

a027818 n = (n + 1) * a007318' (n + 6) 6

-- Reinhard Zumkeller, Aug 31 2014

(PARI) a(n) = (n+1)*binomial(n+6, 6) \\ Charles R Greathouse IV, Jun 11 2015

CROSSREFS

Cf. A093564 ((7, 1) Pascal, column m=7). Partial sums of A050403.

Cf. A062190, A007813, A000142, A245334.

Sequence in context: A008451 A033276 A006858 * A054149 A273182 A025607

Adjacent sequences:  A027815 A027816 A027817 * A027819 A027820 A027821

KEYWORD

nonn,easy

AUTHOR

thi ngoc dinh (via R. K. Guy)

STATUS

approved

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Last modified February 20 15:02 EST 2018. Contains 299380 sequences. (Running on oeis4.)