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A115284
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Correlation triangle of 4-C(1,n)-2*C(0,n) (A113311).
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2
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1, 3, 3, 4, 10, 4, 4, 15, 15, 4, 4, 16, 26, 16, 4, 4, 16, 31, 31, 16, 4, 4, 16, 32, 42, 32, 16, 4, 4, 16, 32, 47, 47, 32, 16, 4, 4, 16, 32, 48, 58, 48, 32, 16, 4, 4, 16, 32, 48, 63, 63, 48, 32, 16, 4, 4, 16, 32, 48, 64, 74, 64, 48, 32, 16, 4
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Row sums are the coordination sequence for cubic lattice A005899. Diagonal sums are A115285. T(2n,n) is A113770. T(2n,n)-T(2n,n+1) is 1,6,10,10,10,.... (10-4C(1,n)-5C(0,n)).
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FORMULA
| G.f.: (1+x)^2*(1+x*y)^2/((1-x)(1-x*y)(1-x^2*y)); Number triangle T(n, k)=sum{j=0..n, [j<=k]*(4-C(1, k-j)-2C(0, k-j))*[j<=n-k]*((4-C(1, n-k-j)-2C(0, n-k-j))}.
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EXAMPLE
| Triangle begins
1;
3, 3;
4, 10, 4;
4, 15, 15, 4;
4, 16, 26, 16, 4;
4, 16, 31, 31, 16, 4;
4, 16, 32, 42, 32, 16, 4;
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CROSSREFS
| Sequence in context: A132319 A130626 A175796 * A202869 A202871 A144626
Adjacent sequences: A115281 A115282 A115283 * A115285 A115286 A115287
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jan 19 2006
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