OFFSET
0,2
COMMENTS
Define a triangle U(n,k) with U(n,0) = n*(n+1) + 1 for n>=0 and U(r,c) = U(r-1,c-1) + U(r-1,c). The sum of the terms in row n is a(n). The first rows are 1; 3, 3; 7, 6, 7; 13, 13, 13, 13; 21, 26, 26, 26, 21; row sums are 1, 6, 20, 52, 120. - J. M. Bergot, Feb 15 2013
This triangle is now A222405. - N. J. A. Sloane, Feb 18 2013
FORMULA
a(n) = 9*2^n - 4n - 8 (conjectured). - Ralf Stephan, Feb 13 2004
Conjectures from Colin Barker, Feb 17 2016: (Start)
a(n) = 4*a(n-1)-5*a(n-2)+2*a(n-3) for n>2.
G.f.: (1+x)^2 / ((1-x)^2*(1-2*x)).
(End)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved