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

1,4

References

A. Errera, Analysis situs: Un problème d'énumération, Memoires Acad. Bruxelles (1931), Serie 2, Vol. 11, No. 6, 26pp.

Links

Table of n, a(n) for n=1..69.

Formula

Sum_{k, 1<=k<=n} T(n,k) = A022553(n); Sum_{k, 1<=k<=n}k*T(n,k) = A002996(n).

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

Example

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;

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 *)

Crossrefs

Cf. A000108, A000150, A050181, A050182, A050183, A050184, A050185.

Sequence in context: A143445 A133727 A103185 * A114596 A083417 A021479

Adjacent sequences: A130510 A130511 A130512 * A130514 A130515 A130516

Keyword

nonn,tabl

Author

Philippe Deléham, Aug 08 2007

Extensions

Edited by N. J. A. Sloane, Oct 08 2007

Status

approved