A027178 - OEIS

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, 4831838084, 9663676288, 19327352700, 38654705528

(list; graph; refs; listen; history; text; internal format)

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..32.

FORMULA

a(n) = 9*2^n - 4*n - 8. - Ralf Stephan, Feb 13 2004 [proved by Christian Krause, May 14 2026]

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)

MAPLE

A027178 := proc(n)

add(A027170(n, k), k=0..n) ;

end proc: