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

0,1

Links

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

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).

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 *)

Prog

(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

Crossrefs

Cf. A052216.

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

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

T(n,0) gives A052539.

Sequence in context: A280373 A324612 A243189 * A345430 A214124 A103041

Adjacent sequences: A055233 A055234 A055235 * A055237 A055238 A055239

Keyword

easy,nonn,tabl

Author

Henry Bottomley, Jun 22 2000

Status

approved