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A073213 Sum of two powers of 17.

%I A073213 #31 Apr 09 2025 19:41:23
%S A073213 2,18,34,290,306,578,4914,4930,5202,9826,83522,83538,83810,88434,
%T A073213 167042,1419858,1419874,1420146,1424770,1503378,2839714,24137570,
%U A073213 24137586,24137858,24142482,24221090,25557426,48275138,410338674,410338690,410338962,410343586,410422194,411758530,434476242,820677346
%N A073213 Sum of two powers of 17.
%H A073213 T. D. Noe, <a href="/A073213/b073213.txt">Rows n = 0..100 of triangle, flattened</a>
%F A073213 T(n,m) = 17^n + 17^m, n = 0, 1, 2, 3, ..., m = 0, 1, 2, 3, ... n.
%F A073213 Bivariate g.f.: (2 - 18*x)/((1 - x)*(1 - 17*x)*(1 - 17*x*y)). - _J. Douglas Morrison_, Jul 26 2021
%e A073213 T(2,0) = 17^2 + 17^0 = 290.
%e A073213 Table T(n,m) begins:
%e A073213       2;
%e A073213      18,    34;
%e A073213     290,   306,   578;
%e A073213    4914,  4930,  5202,  9826;
%e A073213   83522, 83538, 83810, 88434, 167042;
%e A073213   ...
%t A073213 Flatten[Table[Table[17^n + 17^m, {m, 0, n}], {n, 0, 7}]] (* _T. D. Noe_, Jun 18 2013 *)
%t A073213 Union[Total/@Tuples[17^Range[0,10],2]] (* _Harvey P. Dale_, Apr 09 2015 *)
%o A073213 (Python)
%o A073213 from math import isqrt
%o A073213 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
%Y A073213 Cf. A001026 (powers of 17).
%Y A073213 Equals twice A073221.
%Y A073213 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).
%K A073213 easy,nonn,tabl
%O A073213 0,1
%A A073213 _Jeremy Gardiner_, Jul 20 2002