login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A050486 a(n) = binomial(n+6,6)*(2n+7)/7. 21
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, 22915728, 28001193 (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

2*a(n) is number of ways to place 6 queens on an (n+6) X (n+6) chessboard so that they diagonally attack each other exactly 15 times. The maximal possible attack number, p=binomial(k,2)=15 for k=6 queens, is achievable only when all queens are on the same diagonal. In graph-theory representation they thus form a corresponding complete graph. - Antal Pinter, Dec 27 2015

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 entries for 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

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) for n>7. - Wesley Ivan Hurt, Jan 01 2016

MAPLE

A050486:=n->binomial(n+6, 6)*(2*n+7)/7: seq(A050486(n), n=0..50); # Wesley Ivan Hurt, Jan 01 2016

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 )

Table[SeriesCoefficient[(1 + x)/(1 - x)^8, {x, 0, n}], {n, 0, 28}] (* or *)

Table[Binomial[n + 6, 6] (2 n + 7)/7, {n, 0, 30}] (* Michael De Vlieger, Dec 31 2015 *)

PROG

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

(PARI) a(n)=binomial(n+6, 6)*(2*n+7)/7 \\ Charles R Greathouse IV, Sep 24 2015

(Python)

A050486_list, m = [], [2]+[1]*7

for _ in range(10**2):

    A050486_list.append(m[-1])

    for i in range(7):

        m[i+1] += m[i] # Chai Wah Wu, Jan 24 2016

CROSSREFS

Partial sums of A040977, A005585.

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

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

Cf. A053120, A084930.

Sequence in context: A161457 A162212 A161733 * A267176 A267171 A266763

Adjacent sequences:  A050483 A050484 A050485 * A050487 A050488 A050489

KEYWORD

nonn,easy

AUTHOR

Barry E. Williams, Dec 26 1999

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 9 04:50 EST 2016. Contains 278960 sequences.