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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A102916 Triangle, read by rows, where the antidiagonals are formed by interleaving the rows of triangle A102098 with the rows of its matrix square (A102920). 4
1, 1, 2, 1, 4, 3, 3, 8, 9, 4, 7, 40, 27, 16, 5, 36, 152, 189, 64, 25, 6, 139, 1128, 999, 576, 125, 36, 7, 1036, 6200, 9720, 3904, 1375, 216, 49, 8, 5711, 61120, 69687, 47040, 11375, 2808, 343, 64, 9, 56355, 442552, 857466, 416704, 163500, 27432, 5145, 512 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Column 0 is A102917, the interleaving of A082162 with A102921. Under matrix cube, triangle A102098 shifts each column up 1 row.

LINKS

Table of n, a(n) for n=0..52.

FORMULA

G.f. for column k: T(k, k) = k+1 = Sum_{n>=0} T(n+k, k)*x^n*Product_{j=k..[n/2+k]} (1-(j+1)*x).

EXAMPLE

Rows begin:

[1],

[1,2],

[1,4,3],

[3,8,9,4],

[7,40,27,16,5],

[36,152,189,64,25,6],

[139,1128,999,576,125,36,7],

[1036,6200,9720,3904,1375,216,49,8],

[5711,61120,69687,47040,11375,2808,343,64,9],...

The antidiagonals are formed by interleaving the

rows of triangle A102098:

[1],

[1,2],

[7,8,3],

[139,152,27,4],...

with the rows of the matrix square of A102098,

which is triangle A102920:

[1],

[3,4],

[36,40,9],

[1036,1128,189,16],...

G.f. for Column 0 (A102917): 1 = 1*(1-x) + 1*x*(1-x)

+ 1*x^2*(1-x)(1-2x) + 3*x^3*(1-x)(1-2x)

+ 7*x^4*(1-x)(1-2x)(1-3x) + 36*x^5*(1-x)(1-2x)(1-3x) +...

+ A082162(n)*x^(2n)*(1-x)(1-2x)*..*(1-(n+1)x)

+ A102921(n)*x^(2n+1)*(1-x)(1-2x)*..*(1-(n+1)x) + ...

G.f. for Column 1 (A102918): 2 = 2*(1-2x) + 4*x*(1-2x)

+ 8*x^2*(1-2x)(1-3x) + 40*x^3*(1-2x)(1-3x)

+ 152*x^4*(1-2x)(1-3x)(1-4x) + 1128*x^5*(1-2x)(1-3x)(1-4x) +...

+ T(2n+1,1)*x^(2n)*(1-2x)(1-3x)*..*(1-(n+2)x)

+ T(2n+2,1)*x^(2n+1)*(1-2x)(1-3x)*..*(1-(n+2)x) + ...

PROG

(PARI) {T(n, k)=if(n<k, 0, if(n==k, k+1, polcoeff(k+1-sum(i=k, n-1, T(i, k)*x^i*prod(j=1, (i-k)\2+1, 1-(j+k)*x+x*O(x^n))), n)))}

CROSSREFS

Cf. A102086, A102098, A102920, A102917, A102918.

Sequence in context: A134599 A117235 A159573 * A081234 A105239 A261366

Adjacent sequences:  A102913 A102914 A102915 * A102917 A102918 A102919

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Jan 21 2005

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 October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)