A073211 Sum of two powers of 11.

2, 12, 22, 122, 132, 242, 1332, 1342, 1452, 2662, 14642, 14652, 14762, 15972, 29282, 161052, 161062, 161172, 162382, 175692, 322102, 1771562, 1771572, 1771682, 1772892, 1786202, 1932612, 3543122, 19487172, 19487182, 19487292, 19488502, 19501812, 19648222, 21258732, 38974342

Offset: 0

Author

Jeremy Gardiner, Jul 20 2002

Keywords

• easy
• nonn
• tabl

Examples

			T(2,0) = 11^2 + 11^0 = 122.
Table T(n,m) begins:
      2;
     12,    22;
    122,   132,   242;
   1332,  1342,  1452,  2662;
  14642, 14652, 14762, 15972, 29282;
  ...
		

Links

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

Crossrefs

Cf. A001020 (powers of 11).

Equals twice A073219.

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), A194887 (12), A072390 (13), A055261 (16), A073213 (17), A073214 (19), A073215 (23).

Programs

Mathematica

t = 11^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 A073211(n): return 11**(a:=(k:=isqrt(m:=n<<1))+(m>k*(k+1))-1)+11**(n-1-(a*(a+1)>>1)) # Chai Wah Wu, Apr 09 2025

Formula

T(n,m) = 11^n + 11^m, n = 0, 1, 2, 3, ..., m = 0, 1, 2, 3, ... n.

Bivariate g.f.: (2 - 12*x)/((1 - x)*(1 - 11*x)*(1 - 11*x*y)). - J. Douglas Morrison, Jul 26 2021