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 A003983 Array read by antidiagonals with T(n,k) = min(n,k). 34
 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 3, 2, 1, 1, 2, 3, 3, 2, 1, 1, 2, 3, 4, 3, 2, 1, 1, 2, 3, 4, 4, 3, 2, 1, 1, 2, 3, 4, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 7, 6, 5, 4, 3, 2, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Also, "correlation triangle" for the constant sequence 1. - Paul Barry, Jan 16 2006 Antidiagonal sums are in A002620. As a triangle, row sums are A002620. T(2n,n)=n+1. Diagonal sums are A001399. Construction: Take antidiagonal triangle of MM^T where M is the sequence array for the constant sequence 1 (lower triangular matrix with all 1's). - Paul Barry, Jan 16 2006 Zeta[2,k/p]+Zeta[2,(p-k)/p]=(Pi/Sin[(Pi*a(n))/p])^2, where p=2,3,4, k=1..p-1. - Artur Jasinski, Mar 07 2010 From Franklin T. Adams-Watters, Sep 25 2011: (Start) As a triangle, count up to ceiling(n/2) and back down again (repeating the central term when n is even). When the first two instances of each number are removed from the sequence, the original sequence is recovered. (End) LINKS Reinhard Zumkeller, Rows n=1..100 of triangle, flattened FORMULA Number triangle T(n, k)=sum{j=0..n, [j<=k][j<=n-k]}. - Paul Barry, Jan 16 2006 G.f.: 1/((1-x)*(1-x*y)*(1-x^2*y)). - Christian G. Bower, Jan 17 2006 a(n)=min(floor( 1/2 + sqrt(2*n))-(2*n + round(sqrt(2*n)) - round(sqrt(2*n))^2)/2+1,(2*n + round(sqrt(2*n)) - round(sqrt(2*n))^2)/2). - Leonid Bedratyuk, Dec 13 2009 EXAMPLE Triangle version begins 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 3, 2, 1, 1, 2, 3, 3, 2, 1, 1, 2, 3, 4, 3, 2, 1, 1, 2, 3, 4, 4, 3, 2, 1, 1, 2, 3, 4, 5, 4, 3, 2, 1 MAPLE a(n)=min(floor( 1/2 + sqrt(2*n))-(2*n + round(sqrt(2*n)) - round(sqrt(2*n))^2)/2+1, (2*n + round(sqrt(2*n)) - round(sqrt(2*n))^2)/2) # Leonid Bedratyuk, Dec 13 2009 MATHEMATICA aa = {}; Do[Do[AppendTo[aa, (p/Pi) ArcSin[Sqrt[1/((1/Pi^2) (Zeta[2, k/p] + Zeta[2, (p - k)/p]))]]], {k, 1, p - 1}], {p, 2, 50}]; N[aa, 50] (* Artur Jasinski, Mar 07 2010 *) Flatten[Table[Min[n-k+1, k], {n, 1, 14}, {k, 1, n}]] (* Jean-François Alcover, Feb 23 2012 *) PROG (Haskell) a003983 n k = a003983_tabl !! (n-1) !! (k-1) a003983_tabl = map a003983_row [1..] a003983_row n = hs ++ drop m (reverse hs)    where hs = [1..n' + m]          (n', m) = divMod n 2 -- Reinhard Zumkeller, Aug 14 2011 (PARI) T(n, k) = min(n, k) \\ Charles R Greathouse IV, Feb 06 2017 CROSSREFS Cf. A002620, A001399, A087062, A115236, A115237, A124258, A006752, A120268, A173945, A173947, A173948, A173949, A173953, A173954, A173955, A173973, A173982-A173986, A004197. Sequence in context: A113453 A245851 A230596 * A087062 A204026 A110537 Adjacent sequences:  A003980 A003981 A003982 * A003984 A003985 A003986 KEYWORD tabl,nonn,easy,nice AUTHOR EXTENSIONS More terms from Larry Reeves (larryr(AT)acm.org), Nov 08 2000 Entry revised by N. J. A. Sloane, Dec 05 2006 STATUS approved

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