A027178 a(n) = T(n,0) + T(n,1) + ... + T(n,n), T given by A027170.

1, 6, 20, 52, 120, 260, 544, 1116, 2264, 4564, 9168, 18380, 36808, 73668, 147392, 294844, 589752, 1179572, 2359216, 4718508, 9437096, 18874276, 37748640, 75497372, 150994840, 301989780, 603979664, 1207959436, 2415918984

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

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

Crossrefs

Cf. A222405.

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)