login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A140818 Coefficients of Hodge diamond binomial 'X' matrices as polynomials: matrix example; M={{1,0,1}. {0,2,0], {1,0,1}: M(d, x, y)= Sum[Sum[If[n == m, Binomial[d - 1, m - 1], If[n == d - m + 1, Binomial[d - 1, n - 1], 0]]*x^(n - 1)*y^(m - 1), {n, 1, d}], {m, 1, d}] . 0
1, 2, 2, 2, 2, 2, 2, 6, 6, 2, 2, 8, 6, 8, 2, 2, 10, 20, 20, 10, 2, 2, 12, 30, 20, 30, 12, 2, 2, 14, 42, 70, 70, 42, 14, 2, 2, 16, 56, 112, 70, 112, 56, 16, 2, 2, 18, 72, 168, 252, 252, 168, 72, 18, 2 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Apparently the same as A139813. - Georg Fischer, Nov 02 2018

LINKS

Table of n, a(n) for n=1..55.

FORMULA

M(d, x, y)= Sum[Sum[If[n == m, Binomial[d - 1, m - 1], If[n == d - m + 1, Binomial[d - 1, n - 1], 0]]*x^(n - 1)*y^(m - 1), {n, 1, d}], {m, 1, d}] ; a(n,m)=Coefficients(M(n,x,1)).

EXAMPLE

{1},

{2, 2},

{2, 2, 2},

{2, 6, 6, 2},

{2, 8, 6, 8, 2},

{2, 10, 20, 20, 10, 2},

{2, 12, 30, 20, 30, 12, 2},

{2, 14, 42, 70, 70, 42, 14, 2},

{2, 16, 56, 112, 70, 112, 56, 16, 2},

{2, 18, 72, 168, 252, 252, 168, 72, 18, 2}.

MATHEMATICA

Clear[M, y, x] M[d_, x_, y_] := Sum[Sum[If[n == m, Binomial[d - 1, m - 1], If[n == d - m + 1, Binomial[ d - 1, n - 1], 0]]*x^(n - 1)*y^(m - 1), {n, 1, d}], {m, 1, d}] Table[CoefficientList[M[d, x, 1], x], {d, 1, 10}] Flatten[%] Table[Apply[Plus, CoefficientList[M[d, x, 1], x]], {d, 1, 10}]

CROSSREFS

Cf. A139813, A140685.

Sequence in context: A244461 A343925 A105255 * A139813 A172009 A299150

Adjacent sequences:  A140815 A140816 A140817 * A140819 A140820 A140821

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula and Mats Granvik, Jul 16 2008

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 28 12:47 EST 2021. Contains 349403 sequences. (Running on oeis4.)