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A115268 Correlation triangle for floor((n+4)/4). 3
1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 3, 2, 2, 2, 3, 3, 3, 3, 2, 2, 4, 4, 4, 4, 4, 2, 2, 4, 5, 5, 5, 5, 4, 2, 3, 4, 6, 6, 8, 6, 6, 4, 3, 3, 5, 6, 7, 9, 9, 7, 6, 5, 3, 3, 6, 7, 8, 10, 12, 10, 8, 7, 6, 3, 3, 6, 8, 9, 11, 13, 13, 11, 9, 8, 6, 3, 4, 6, 9, 10, 14, 14, 16, 14, 14, 10, 9, 6, 4 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are A115269. Diagonal sums are A115270. T(2n,n) is A115271. T(2n,n)-T(2n,n-1) is 1,1,1,0,2,2,2,0,3,3,3,0,...

LINKS

Table of n, a(n) for n=0..90.

FORMULA

G.f.: (1+x+x^2+x^3)(1+xy+x^2*y^2+x^3*y^3)/((1-x^4)^2*(1-x^4*y^4)^2*(1-x^2*y)); Number triangle T(n, k)=sum{j=0..n, [j<=k]*floor((k-j+4)/4)*[j<=n-k]*floor((n-k-j+4)/4)}.

EXAMPLE

Triangle begins

1;

1,1;

1,2,1;

1,2,2,1;

2,2,3,2,2;

2,3,3,3,3,2;

2,4,4,4,4,4,2;

2,4,5,5,5,5,4,2;

3,4,6,6,8,6,6,4,3;

3,5,6,7,9,9,7,6,5,3;

3,6,7,8,10,12,10,8,7,6,3;

3,6,8,9,11,13,13,11,9,8,6,3;

CROSSREFS

Sequence in context: A029435 A089643 A185090 * A103610 A305875 A109705

Adjacent sequences:  A115265 A115266 A115267 * A115269 A115270 A115271

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Jan 18 2006

STATUS

approved

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Last modified October 26 18:30 EDT 2021. Contains 348268 sequences. (Running on oeis4.)