%I #34 Jun 26 2022 09:17:06

%S 2,4,6,10,12,18,28,30,36,54,82,84,90,108,162,244,246,252,270,324,486,

%T 730,732,738,756,810,972,1458,2188,2190,2196,2214,2268,2430,2916,4374,

%U 6562,6564,6570,6588,6642,6804,7290,8748,13122,19684,19686,19692,19710

%N Sums of two powers of 3.

%H T. D. Noe, <a href="/A055235/b055235.txt">Rows n = 0..100 of triangle, flattened</a>

%F a(n+1) = 3^(n-trinv(n)*(trinv(n)+1)/2)+3^trinv(n), where trinv(n) = floor((sqrt(1+8*n)-1)/2) = A003056(n) and n-trinv(n)*(trinv(n)+1)/2 = A002262(n). [corrected by _M. F. Hasler_, Oct 08 2011]

%F Regarded as a triangle, T(n, k) = 3^n + 3^k, because 3^n + 3^n < 3^(n+1) + 3^0 for all n > 0.

%t mx = 10; Sort[Flatten[Table[3^x + 3^y, {y, 0, mx}, {x, 0, y}]]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 20 2011 *)

%t f[n_] := Block[{t = Floor[(Sqrt[1 + 8 (n - 1)] - 1)/2]}, 3^(n - 1 - t*(t + 1)/2) + 3^t]; Array[f, 49] (* _Robert G. Wilson v_, Oct 08 2011 *)

%o (PARI) for( n=0,5, for(k=0,n, print1(3^n+3^k",")))

%o (PARI) A055235(n)={ my( t=(sqrtint(8*n-7)-1)\2); 3^t+3^(n-1-t*(t+1)/2) } \\ _M. F. Hasler_, Oct 08 2011

%Y Cf. A052216.

%Y Partial sums of A135293.

%K easy,nonn,tabl

%O 0,1

%A _Henry Bottomley_, Jun 22 2000