A055235 Sums of two powers of 3.

2, 4, 6, 10, 12, 18, 28, 30, 36, 54, 82, 84, 90, 108, 162, 244, 246, 252, 270, 324, 486, 730, 732, 738, 756, 810, 972, 1458, 2188, 2190, 2196, 2214, 2268, 2430, 2916, 4374, 6562, 6564, 6570, 6588, 6642, 6804, 7290, 8748, 13122, 19684, 19686, 19692, 19710

Offset: 0

Author

Henry Bottomley, Jun 22 2000

Keywords

• easy
• nonn
• tabl
• changed

Links

• T. D. Noe, Rows n = 0..100 of triangle, flattened

Crossrefs

Cf. A002262, A003056, A052216.

Partial sums of A135293.

Programs

Mathematica

mx = 10; Sort[Flatten[Table[3^x + 3^y, {y, 0, mx}, {x, 0, y}]]] (* Vladimir Joseph Stephan Orlovsky, Apr 20 2011 *)
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 *)
Total/@Tuples[3^Range[0,10],2]//Union (* Harvey P. Dale, Aug 28 2025 *)

PARI

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

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

Python

from math import isqrt
def A055235(n): return 3**(a:=(k:=isqrt(m:=n<<1))+(m>k*(k+1))-1)+3**(n-1-(a*(a+1)>>1)) # Chai Wah Wu, Apr 08 2025

Formula

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]

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.