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 A115265 Correlation triangle for floor((n+3)/3). 1
 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 3, 3, 3, 2, 2, 4, 4, 4, 4, 2, 3, 4, 5, 7, 5, 4, 3, 3, 5, 6, 8, 8, 6, 5, 3, 3, 6, 7, 9, 11, 9, 7, 6, 3, 4, 6, 8, 12, 12, 12, 12, 8, 6, 4, 4, 7, 9, 13, 15, 15, 15, 13, 9, 7, 4 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are A115266. Diagonal sums are A115267. T(2n,n) is A092353. T(2n,n)-T(2n,n+1)=A087508(n+1). LINKS FORMULA G.f.: (1+x+x^2)(1+xy+x^2*y^2)/((1-x^3)^2*(1-x^3*y^3)^2*(1-x^2*y)). T(n, k) = sum{j=0..n, [j<=k]*floor((k-j+3)/3)*[j<=n-k]*floor((n-k-j+3)/3)}. EXAMPLE Triangle begins 1; 1,1; 1,2,1; 2,2,2,2; 2,3,3,3,2; 2,4,4,4,4,2; 3,4,5,7,5,4,3; 3,5,6,8,8,6,5,3; 3,6,7,9,11,9,7,6,3; MATHEMATICA T[n_, k_] := Sum[Boole[j <= k] * Floor[(k - j + 3)/3] * Boole[j <= n-k] * Floor[(n - k - j + 3)/3], {j, 0, n}]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jul 15 2017 *) CROSSREFS Sequence in context: A024939 A024937 A143977 * A105223 A025859 A031281 Adjacent sequences:  A115262 A115263 A115264 * A115266 A115267 A115268 KEYWORD easy,nonn,tabl AUTHOR Paul Barry, Jan 18 2006 STATUS approved

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Last modified May 17 21:11 EDT 2021. Contains 343990 sequences. (Running on oeis4.)