A055257 Sums of two powers of 6.

2, 7, 12, 37, 42, 72, 217, 222, 252, 432, 1297, 1302, 1332, 1512, 2592, 7777, 7782, 7812, 7992, 9072, 15552, 46657, 46662, 46692, 46872, 47952, 54432, 93312, 279937, 279942, 279972, 280152, 281232, 287712, 326592, 559872, 1679617, 1679622, 1679652, 1679832

Offset: 0

Author

Henry Bottomley, Jun 22 2000

Keywords

• easy
• nonn
• tabl

Links

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

Crossrefs

Cf. A052216.

Programs

Mathematica

t = 6^Range[0, 9]; Select[Union[Flatten[Table[i + j, {i, t}, {j, t}]]], # <= t[[-1]] + 1 &] (* T. D. Noe, Oct 09 2011 *)

Python

from math import isqrt
def A055257(n): return 6**(a:=(k:=isqrt(m:=n<<1))+(m>k*(k+1))-1)+6**(n-1-(a*(a+1)>>1)) # Chai Wah Wu, Apr 08 2025

Formula

a(n) = 6^(n-trinv(n))+6^trinv(n), where trinv(n) = floor((1+sqrt(1+8*n))/2) = A002262(n) and n-trinv(n) = A003056(n)

Regarded as a triangle T(n, k) = 6^n + 6^k, so as a sequence a(n) = 6^A002262(n) + 6^A003056(n).