A061801 a(n) = (7*6^n - 2)/5.

1, 8, 50, 302, 1814, 10886, 65318, 391910, 2351462, 14108774, 84652646, 507915878, 3047495270, 18284971622, 109709829734, 658258978406, 3949553870438, 23697323222630, 142183939335782, 853103636014694

Offset: 0

Author

Amarnath Murthy, May 28 2001

Keywords

• nonn
• easy

Comments

Sum of n-th row of triangle of powers of 6: 1; 1 6 1; 1 6 36 6 1; 1 6 36 216 36 6 1; ....

Examples

			a(2) = 50 = 1 + 6 + 36 + 6 + 1.
G.f. = 1 + 8*x + 50*x^2 + 302*x^3 + 1814*x^4 + 10886*x^5 + 65318*x^6 + ...
		

Links

• Harry J. Smith, Table of n, a(n) for n=0,...,200

Crossrefs

Cf. A057651, A112468, A112739.

Programs

Maple

restart:g:=(1+x)/(1-6*x)/(1-x): gser:=series(g, x=0, 43): seq(coeff(gser, x, n), n=0..30); # Zerinvary Lajos, Jan 11 2009

PARI

{ for (n=0, 200, write("b061801.txt", n, " ", (7*6^n - 2)/5) ) } \\ Harry J. Smith, Jul 28 2009

Formula

G.f.: (1+x)/(1-6*x)/(1-x) [Zerinvary Lajos, Jan 11 2009]

a(n) = 6*a(n-1) + 2, a(0) = 1. - Philippe Deléham, Feb 23 2014

a(n) = Sum_{k=0..n} A112468(n,k)*7^k. - Philippe Deléham, Feb 23 2014

Extensions

More terms from Larry Reeves (larryr(AT)acm.org) and Jason Earls, May 28 2001.

Better description from Dean Hickerson, Jun 06 2001

Divided g.f. by x to match the offset. - Philippe Deléham, Feb 23 2014