A061801 - OEIS

%I #23 Aug 25 2022 09:17:13

%S 1,8,50,302,1814,10886,65318,391910,2351462,14108774,84652646,

%T 507915878,3047495270,18284971622,109709829734,658258978406,

%U 3949553870438,23697323222630,142183939335782,853103636014694

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

%C 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; ....

%H Harry J. Smith, <a href="/A061801/b061801.txt">Table of n, a(n) for n=0,...,200</a>

%F G.f.: (1+x)/(1-6*x)/(1-x) [_Zerinvary Lajos_, Jan 11 2009]

%F a(n) = 6*a(n-1) + 2, a(0) = 1. - _Philippe Deléham_, Feb 23 2014

%F a(n) = Sum_{k=0..n} A112468(n,k)*7^k. - _Philippe Deléham_, Feb 23 2014

%e a(2) = 50 = 1 + 6 + 36 + 6 + 1.

%e G.f. = 1 + 8*x + 50*x^2 + 302*x^3 + 1814*x^4 + 10886*x^5 + 65318*x^6 + ...

%p 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

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

%Y Cf. A057651, A112468, A112739.

%K nonn,easy

%O 0,2

%A _Amarnath Murthy_, May 28 2001

%E More terms from Larry Reeves (larryr(AT)acm.org) and _Jason Earls_, May 28 2001.

%E Better description from _Dean Hickerson_, Jun 06 2001

%E Divided g.f. by x to match the offset. - _Philippe Deléham_, Feb 23 2014