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

0,1

Links

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

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.

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 *)

Prog

(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

Crossrefs

Cf. A002262, A003056, A052216.

Partial sums of A135293.

Sequence in context: A065385 A244052 A324059 * A083887 A339736 A064374

Adjacent sequences: A055232 A055233 A055234 * A055236 A055237 A055238

Keyword

easy,nonn,tabl

Author

Henry Bottomley, Jun 22 2000

Status

approved