A118181 - OEIS

%I #8 Sep 08 2022 08:45:25

%S 1,2,5,20,137,1622,33293,1182440,72811793,7757988842,1433154521621,

%T 458101483131260,253879024041595289,243453910296759945662,

%U 404765167247068325944349,1164432505878183620543030480

%N Row sums of triangle A118180: a(n) = Sum_{k=0..n} (3^k)^(n-k) for n>=0.

%C Also equals column 0 of the matrix square of triangle A118180, where [A118180^2](n,k) = a(n-k)*(3^k)^(n-k) for n>=k>=0.

%H G. C. Greubel, <a href="/A118181/b118181.txt">Table of n, a(n) for n = 0..90</a>

%F G.f.: A(x) = Sum_{n>=0} x^n/(1-3^n*x).

%e A(x) = 1/(1-x) + x/(1-3x) + x^2/(1-9x) + x^3/(1-27x) + ...

%e = 1 + 2*x + 5*x^2 + 20*x^3 + 137*x^4 + 1622*x^5 + 33293*x^6 +...

%p seq( add(3^(k*(n-k)), k=0..n), n=0..30); # modified by _G. C. Greubel_, Jun 29 2021

%t Table[Sum[3^(k*(n-k)), {k,0,n}], {n,0,30}] (* _G. C. Greubel_, Jun 29 2021 *)

%o (PARI) a(n)=sum(k=0, n, (3^k)^(n-k) );

%o (Magma) [(&+[3^(k*(n-k)): k in [0..n]]): n in [0..30]]; // _G. C. Greubel_, Jun 29 2021

%o (Sage) [sum(3^(k*(n-k)) for k in (0..n)) for n in (0..30)] # _G. C. Greubel_, Jun 29 2021

%Y Cf. A118180 (triangle), A118182 (antidiagonal sums); A118183, A118184.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Apr 15 2006