A055258 Sums of two powers of 7.

2, 8, 14, 50, 56, 98, 344, 350, 392, 686, 2402, 2408, 2450, 2744, 4802, 16808, 16814, 16856, 17150, 19208, 33614, 117650, 117656, 117698, 117992, 120050, 134456, 235298, 823544, 823550, 823592, 823886, 825944, 840350, 941192, 1647086, 5764802, 5764808, 5764850, 5765144, 5767202, 5781608, 5882450, 6588344, 11529602

Offset

0,1

Links

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

Formula

a(n) = 7^(n-trinv(n))+7^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) = 7^n + 7^k, so as a sequence a(n) = 7^A002262(n) + 7^A003056(n).

Mathematica

t = 7^Range[0, 9]; Select[Union[Flatten[Table[i + j, {i, t}, {j, t}]]], # <= t[[-1]] + 1 &] (* T. D. Noe, Oct 09 2011 *)
Total/@Tuples[7^Range[0, 10], 2]//Union (* Harvey P. Dale, Dec 31 2017 *)

Prog

(Python)
from math import isqrt
def A055258(n): return 7**(a:=(k:=isqrt(m:=n<<1))+(m>k*(k+1))-1)+7**(n-1-(a*(a+1)>>1)) # Chai Wah Wu, Apr 08 2025

Crossrefs

Cf. A052216.

Equals 2*A073218.

Sequence in context: A333054 A119752 A111001 * A277649 A192777 A054981

Adjacent sequences: A055255 A055256 A055257 * A055259 A055260 A055261

Keyword

easy,nonn,tabl

Author

Henry Bottomley, Jun 22 2000

Status

approved