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

0,2

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

Links

Table of n, a(n) for n=0..28.

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

Cf. A222405.

Sequence in context: A001211 A122225 A275112 * A264314 A055909 A036596

Adjacent sequences: A027175 A027176 A027177 * A027179 A027180 A027181

Keyword

nonn

Author

Clark Kimberling

Status

approved