A055236 Sums of two powers of 4.

2, 5, 8, 17, 20, 32, 65, 68, 80, 128, 257, 260, 272, 320, 512, 1025, 1028, 1040, 1088, 1280, 2048, 4097, 4100, 4112, 4160, 4352, 5120, 8192, 16385, 16388, 16400, 16448, 16640, 17408, 20480, 32768, 65537, 65540, 65552, 65600, 65792, 66560, 69632, 81920, 131072

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.

T(2n,n) gives 2*A026244.

T(n,n) gives A004171 = 2*A000302.

T(n,0) gives A052539.

Programs

Mathematica

t = 4^Range[0, 9]; Select[Union[Flatten[Table[i + j, {i, t}, {j, t}]]], # <= t[[-1]] + 1 &] (* T. D. Noe, Oct 09 2011 *)
Union[Total/@Tuples[4^Range[0,9], 2]] (* Harvey P. Dale, Mar 25 2012 *)

Python

from math import isqrt
def A055236(n): return (1<<((a:=(k:=isqrt(m:=n<<1))+(m>k*(k+1))-1)<<1))+(1<<(n-1-(a*(a+1)>>1)<<1)) # Chai Wah Wu, Apr 08 2025

Formula

a(n) = 4^(n-trinv(n))+4^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) = 4^n + 4^k, so as a sequence a(n) = 4^A002262(n) + 4^A003056(n).