0,4

Trisection of the Padovan sequence: a(n)=A000931(3n). - Paul Barry (pbarry(AT)wit.ie), Jul 06 2004

a(n+1) gives diagonal sums of Riordan array (1/(1-x),x/(1-x)^3). - Paul Barry (pbarry(AT)wit.ie), Oct 11 2005

a(n+2) is the sum, over all Boolean n-strings, of the product of the lengths of the runs of 1. For example, the Boolean 7-string (0,1,1,0,1,1,1) has two runs of 1s. Their lengths, 2 and 3, contribute a product of 6 to a(9). The 8 Boolean 3-strings contribute to a(5) as follows: 000 (empty product), 001, 010, 100, 101 all contribute 1, 011 and 110 contribute 2, 111 contributes 3. - David Callan (callan(AT)stat.wisc.edu), Nov 29 2007

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 904

a(n)=3a(n-1)-2a(n-2)+a(n-3).

a(n)=sum{k=0..floor(n/2), binomial(n+k-1, 3k)}. - Paul Barry (pbarry(AT)wit.ie), Jul 06 2004

G.f.: (1-2x)/(1-3x+2x^2-x^3); - Paul Barry (pbarry(AT)wit.ie), Jul 06 2005

[a(n), a(n+1), a(n+2)], n>0 = [0,1,0; 0,0,1; 1,-2,3]^n * [1,1,1]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 27 2008

First differences of A052921.

Sequence in context: A019485 A018914 A129519 this_sequence A024960 A062422 A079864

Adjacent sequences: A034940 A034941 A034942 this_sequence A034944 A034945 A034946

nonn

njas