0,3

Refer to A089378 and A075729 for the definition of hierarchies, subhierarchies and one-step transitions. - Thomas Wieder (wieder.thomas(AT)t-online.de), Feb 28 2004

We may ask for the number of one-step transitions (NOOST) between all unlabeled hierarchies of n elements with the restriction that no subhierarchies are allowed. As an example, consider n = 4 and the hierarchy H1 = [[2,2]] with two elements on level 1 and two on level 2. Starting from H1 the hierarchies [[1, 3]], [[2, 1, 1]], [[1, 2, 1]] can be reached by moving one element only, but [[1, 1, 2]] can not be reached in a one-step transitition. The solution is n = 1, NOOST = 0; n = 2, NOOST = 1; n = 3, NOOST = 4; n = 4, NOOST = 13; n = 5, NOOST = 38; n = 6, NOOST = 104; n = 7, NOOST = 272, n = 8, NOOST = 688; n = 9, NOOST = 1696;. This is sequence A049611. - Thomas Wieder (wieder.thomas(AT)t-online.de), Feb 28 2004

If X_1,X_2,...,X_n are 2-blocks of a (2n+2)-set X then, for n>=1, a(n+1) is the number of (n+2)-subsets of X intersecting each X_i, (i=1,2,...,n). - Milan R. Janjic (agnus(AT)blic.net), Nov 18 2007

Milan Janjic, Two Enumerative Functions

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

Binomial transform of quarter squares A002620(n+1). - Paul Barry (pbarry(AT)wit.ie), May 27 2003

a(n)=sum{k=0..n, C(n, k)Floor((k+1)^2/4) } - Paul Barry (pbarry(AT)wit.ie), May 27 2003

a(n)=2^(n-4)(n^2+5n+2)-0^n/8. - Paul Barry (pbarry(AT)wit.ie), Jun 09 2003

a(n+2) = A001787(n+2) + A001788(n). Floretion Algebra Multiplication Program, FAMP Code: 1vessum(pos)seq[A] (= (a(n)), from 2nd term), 1vessum(neg)seq[A], and 1vessumseq[A] with A = + .5'i + .5i' + .5'ij' + .5'ki' + 2e. Sumtype is set to: default (ver. f) - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Aug 02 2005

Row sums of triangle A133729 = (1, 4, 13, 38,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 21 2007

a(n+1)= A055252(n, 0), n >= 0. Row sums of triangle A055249.

Cf. A058396, A001793.

Cf. A089378, A075729.

Cf. A133729.

Sequence in context: A024450 A047094 A089092 this_sequence A084851 A094706 A056014

Adjacent sequences: A049608 A049609 A049610 this_sequence A049612 A049613 A049614

nonn

Clark Kimberling (ck6(AT)evansville.edu)