1,2

Number of 1's in the n X n lower Hessenberg (0,1)-matrix (i.e. the matrix having 1's on or below the superdiagonal and 0's above the superdiagonal).

If a 2-set Y and 2-set Z, having one element in common, are subsets of an n-set X then a(n-2) is the number of 3-subests of X intersecting both Y and Z. - Milan R. Janjic (agnus(AT)blic.net), Oct 03 2007

D. D. Olesky, B. L. Shader and P. van den Driessche, Permanents of Hessenberg (0,1)-matrices, Electronic Journal of Combinatorics, 12 (2005) #R70.

J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478.

Milan Janjic, Two Enumerative Functions

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 471

W. F. Klostermeyer, M. E. Mays, L. Soltes and G. Trapp, A Pascal rhombus, Fibonacci Quarterly, 35 (1997), 318-328.

G.f.: A(x) = x*(1+x-x^2)/(1-x)^3.

With offset 0, this is C(n+3, 2)-2 = (n^2+5n+2)/2 - Paul Barry (pbarry(AT)wit.ie), Feb 27 2003

With offset 5, this is C(n, 0)-2C(n, 1)+C(n, 2), the binomial transform of (1, -2, 1, 0, 0, 0, ....). - Paul Barry (pbarry(AT)wit.ie), Jul 01 2003

Row sums of triangle A131818 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 27 2007

Binomial transform of (1, 3, 1, 0, 0, 0,...). Also equals A130296 * [1,2,3,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 27 2007

Row sums of triangle A134225 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 14 2007

a(n) = A000217(n+1) - 2. - Omar E. Pol (info(AT)polprimos.com), Apr 23 2008

a(n) = ((n(n+3)+2)/2)-2. - Omar E. Pol (info(AT)polprimos.com), May 18 2008

a:=array(1...53): a[1]:=1: print(1, a[1]); for i from 2 to 53 do a[i]:= a[i-1]+(binomial(i+1, i)):print(i, a[i]); od: - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 27 2007

with (combinat):a:=n->sum(fibonacci(2, i), i=0..n):seq(a(n)-2, n=2..54); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 25 2008

a:=n->sum(k, k=2..n):seq(a(n)/2+sum(k, k=3..n)/2, n=2..54); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 10 2008

Triangular numbers (A000217) minus two. a(n)=T(3, n-2), array T as in A049600.

Cf. A000096, A027379. Third diagonal of triangle in A059317.

Cf. A113452-A113455.

Cf. A130296, A131818.

Cf. A134225.

Sequence in context: A127264 A004081 A130236 this_sequence A064609 A056738 A071994

Adjacent sequences: A034853 A034854 A034855 this_sequence A034857 A034858 A034859

nonn

njas

More terms from Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 12 2006