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A050486 C(n+6,6)*(2n+7)/7. 17
1, 9, 44, 156, 450, 1122, 2508, 5148, 9867, 17875, 30888, 51272, 82212, 127908, 193800, 286824, 415701, 591261, 826804, 1138500, 1545830, 2072070, 2744820, 3596580, 4665375, 5995431, 7637904, 9651664, 12104136, 15072200, 18643152 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

If a 2-set Y and an (n-3)-set Z are disjoint subsets of an n-set X then a(n-8) is the number of 8-subsets of X intersecting both Y and Z. - Milan Janjic, Sep 08 2007

7-dimensional square numbers, sixth partial sums of binomial transform of [1,2,0,0,0,...]. a(n)=sum{i=0,n,C(n+6,i+6)*b(i)}, where b(i)=[1,2,0,0,0,...]. [Borislav St. Borisov (b.st.borisov(AT)abv.bg), Mar 05 2009]

REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Milan Janjic, Two Enumerative Functions

Index entries for sequences related to Chebyshev polynomials.

Index to sequences with linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1)

FORMULA

a(n)= ((-1)^n)*A053120(2*n+7, 7)/64 (1/64 of eighth unsigned column of Chebyshev T-triangle, zeros omitted).

G.f.: (1+x)/(1-x)^8.

a(n) = 2*C(n+7, 7)-C(n+6, 6). - Paul Barry, Mar 04 2003

a(n) = C(n+6,6)+2*C(n+6,7). [Borislav St. Borisov (b.st.borisov(AT)abv.bg), Mar 05 2009]

a(n) = ((-1)^n)*A084930(n+3, 3)/64. Compare with the first line above. - Wolfdieter Lang, Aug 04 2014

MATHEMATICA

s1=s2=s3=s4=s5=0; lst={}; Do[s1+=n^2; s2+=s1; s3+=s2; s4+=s3; s5+=s4; AppendTo[lst, s5], {n, 0, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 15 2009 *)

CoefficientList[Series[(1 + x) / (1 - x)^8, {x, 0, 50}], x] (* Vincenzo Librandi, Jun 09 2013 )

PROG

(MAGMA) [Binomial(n+6, 6) + 2*Binomial(n+6, 7): n in [0..35]]; // Vincenzo Librandi, Jun 09 2013

CROSSREFS

Partial sums of A040977, A005585.

Fourth column (s=3, without leading zeros) of A111125. [Wolfdieter Lang, Oct 18 2012]

A084960 (unsigned fourth column divided by 64). - Wolfdieter Lang, Aug 04 2014

Sequence in context: A161457 A162212 A161733 * A213755 A036599 A229404

Adjacent sequences:  A050483 A050484 A050485 * A050487 A050488 A050489

KEYWORD

nonn,easy

AUTHOR

Barry E. Williams, Dec 26 1999

STATUS

approved

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Last modified December 20 10:32 EST 2014. Contains 252241 sequences.