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A099239 Square array read by antidiagonals associated with sections of 1/(1-x-x^k). 4
1, 1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 8, 8, 4, 1, 1, 16, 21, 13, 5, 1, 1, 32, 55, 41, 19, 6, 1, 1, 64, 144, 129, 69, 26, 7, 1, 1, 128, 377, 406, 250, 106, 34, 8, 1, 1, 256, 987, 1278, 907, 431, 153, 43, 9, 1, 1, 512, 2584, 4023, 3292, 1757, 686, 211, 53, 10, 1, 1, 1024, 6765, 12664 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Rows include A099242, A099253. Columns include A034856. Main diagonal is A099240. Sums of antidiagonals are A099241.

LINKS

Table of n, a(n) for n=0..69.

FORMULA

Square array T(n, k)=sum{j=0..n, binomial(k*n-(k-1)(j-1), j)}, n, k>=0. Also, T(n, k)=sum{j=0..n, binomial(k+(n-1)(j+1), n(j+1)-1}, n>0. As a number triangle read by row, this is T(n, k)=sum{j=0..n-k, binomial(k(n-k)-(k-1)(j-1)}. Rows of the square array are generated by 1/((1-x)^k-x). Rows satisfy a(n)=a(n-1)-sum{k=1..n, (-1)^k^C(n, k)a(n-k)}.

EXAMPLE

Rows begin

1,1,1,1,1,1,1,...

1,2,4,8,16,32,... 1-section of 1/(1-x-x) A000079

1,3,8,21,55,..... bisection of 1/(1-x-x^2) A001906

1,4,13,41,129,... trisection of 1/(1-x-x^3) A052529 (essentially)

1,5,19,69,250,... quadrisection of 1/(1-x-x^4) A055991

1,6,26,106,431,.. quintisection of 1/(1-x-x^5) A079675 (essentially)

CROSSREFS

Sequence in context: A247286 A055587 A137743 * A167630 A322264 A009998

Adjacent sequences:  A099236 A099237 A099238 * A099240 A099241 A099242

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Oct 08 2004

STATUS

approved

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Last modified April 21 04:56 EDT 2019. Contains 322310 sequences. (Running on oeis4.)