A130513 Subtriangle of triangle in A051168: remove central column of A051168 and all columns to the right; now read by upwards diagonals.
1, 1, 0, 2, 1, 0, 5, 2, 1, 0, 14, 7, 3, 1, 0, 42, 20, 9, 3, 1, 0, 132, 66, 30, 12, 4, 1, 0, 429, 212, 99, 40, 15, 4, 1, 0, 1430, 715, 333, 143, 55, 18, 5, 1, 0, 4862, 2424, 1144, 497, 200, 70, 22, 5, 1, 0, 16796, 8398, 3978, 1768, 728, 273, 91, 26, 6, 1, 0, 58786, 29372, 13995
Offset: 1
Examples
Triangle T(n,k), 1<=k<=n, begins: 1; 1, 0; 2, 1, 0; 5, 2, 1, 0; 14, 7, 3, 1, 0; 42, 20, 9, 3, 1, 0; 132, 66, 30, 12, 4, 1, 0; 429, 212, 99, 40, 15, 4, 1, 0;
References
- A. Errera, Analysis situs: Un problème d'énumération, Memoires Acad. Bruxelles (1931), Serie 2, Vol. 11, No. 6, 26pp.
Programs
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Mathematica
Table[1/(2n-k) Plus@@ (MoebiusMu[ # ]Binomial[(2n-k)/#,(n-k)/# ]&/@ Divisors[GCD[2n-k,n-k]]),{n,12},{k,n}] (* Wouter Meeussen, Jul 20 2008 *)
Formula
T(n,k) = 1/(2n-k) Sum( d | gcd(2n-k,n-k) = mu(d) C((2n-k)/d,(n-k)/d) ). - Wouter Meeussen, Jul 20 2008
Extensions
Edited by N. J. A. Sloane, Oct 08 2007