A073213 Sum of two powers of 17.

2, 18, 34, 290, 306, 578, 4914, 4930, 5202, 9826, 83522, 83538, 83810, 88434, 167042, 1419858, 1419874, 1420146, 1424770, 1503378, 2839714, 24137570, 24137586, 24137858, 24142482, 24221090, 25557426, 48275138, 410338674, 410338690, 410338962, 410343586, 410422194, 411758530, 434476242, 820677346

Offset: 0

Author

Jeremy Gardiner, Jul 20 2002

Keywords

• easy
• nonn
• tabl

Examples

			T(2,0) = 17^2 + 17^0 = 290.
Table T(n,m) begins:
      2;
     18,    34;
    290,   306,   578;
   4914,  4930,  5202,  9826;
  83522, 83538, 83810, 88434, 167042;
  ...
		

Links

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

Crossrefs

Cf. A001026 (powers of 17).

Equals twice A073221.

Sums of two powers of n: A073423 (0), A007395 (1), A173786 (2), A055235 (3), A055236 (4), A055237 (5), A055257 (6), A055258 (7), A055259 (8), A055260 (9), A052216 (10), A073211 (11), A194887 (12), A072390 (13), A055261 (16), A073214 (19), A073215 (23).

Programs

Mathematica

Flatten[Table[Table[17^n + 17^m, {m, 0, n}], {n, 0, 7}]] (* T. D. Noe, Jun 18 2013 *)
Union[Total/@Tuples[17^Range[0,10],2]] (* Harvey P. Dale, Apr 09 2015 *)

Python

from math import isqrt
def A073213(n): return 17**(a:=(k:=isqrt(m:=n<<1))+(m>k*(k+1))-1)+17**(n-1-(a*(a+1)>>1)) # Chai Wah Wu, Apr 09 2025

Formula

T(n,m) = 17^n + 17^m, n = 0, 1, 2, 3, ..., m = 0, 1, 2, 3, ... n.

Bivariate g.f.: (2 - 18*x)/((1 - x)*(1 - 17*x)*(1 - 17*x*y)). - J. Douglas Morrison, Jul 26 2021