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A073211 Sum of two powers of 11.

%I A073211 #33 Apr 09 2025 14:13:46
%S A073211 2,12,22,122,132,242,1332,1342,1452,2662,14642,14652,14762,15972,
%T A073211 29282,161052,161062,161172,162382,175692,322102,1771562,1771572,
%U A073211 1771682,1772892,1786202,1932612,3543122,19487172,19487182,19487292,19488502,19501812,19648222,21258732,38974342
%N A073211 Sum of two powers of 11.
%H A073211 T. D. Noe, <a href="/A073211/b073211.txt">Rows n = 0..100 of triangle, flattened</a>
%F A073211 T(n,m) = 11^n + 11^m, n = 0, 1, 2, 3, ..., m = 0, 1, 2, 3, ... n.
%F A073211 Bivariate g.f.: (2 - 12*x)/((1 - x)*(1 - 11*x)*(1 - 11*x*y)). - _J. Douglas Morrison_, Jul 26 2021
%e A073211 T(2,0) = 11^2 + 11^0 = 122.
%e A073211 Table T(n,m) begins:
%e A073211       2;
%e A073211      12,    22;
%e A073211     122,   132,   242;
%e A073211    1332,  1342,  1452,  2662;
%e A073211   14642, 14652, 14762, 15972, 29282;
%e A073211   ...
%t A073211 t = 11^Range[0, 9]; Select[Union[Flatten[Table[i + j, {i, t}, {j, t}]]], # <= t[[-1]] + 1 &] (* _T. D. Noe_, Oct 09 2011 *)
%o A073211 (Python)
%o A073211 from math import isqrt
%o A073211 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
%Y A073211 Cf. A001020 (powers of 11).
%Y A073211 Equals twice A073219.
%Y A073211 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).
%K A073211 easy,nonn,tabl
%O A073211 0,1
%A A073211 _Jeremy Gardiner_, Jul 20 2002