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A073214 Sum of two powers of 19.

%I A073214 #34 Apr 09 2025 19:45:31
%S A073214 2,20,38,362,380,722,6860,6878,7220,13718,130322,130340,130682,137180,
%T A073214 260642,2476100,2476118,2476460,2482958,2606420,4952198,47045882,
%U A073214 47045900,47046242,47052740,47176202,49521980,94091762,893871740,893871758,893872100,893878598,894002060,896347838,940917620,1787743478
%N A073214 Sum of two powers of 19.
%H A073214 T. D. Noe, <a href="/A073214/b073214.txt">Rows n = 0..100 of triangle, flattened</a>
%F A073214 T(n,m) = 19^n + 19^m for n >= 0 and m in [0..n].
%F A073214 Bivariate g.f.: (2 - 20*x) / ((1 - x) * (1 - 19*x) * (1 - 19*x*y)). - _J. Douglas Morrison_, Jul 28 2021
%e A073214 T(2,0) = 19^2 + 19^0 = 362.
%e A073214 Table begins:
%e A073214        2;
%e A073214       20,     38;
%e A073214      362,    380,    722;
%e A073214     6860,   6878,   7220,  13718;
%e A073214   130322, 130340, 130682, 137180, 260642;
%e A073214   ...
%t A073214 Flatten[Table[Table[19^n + 19^m, {m, 0, n}], {n, 0, 7}]] (* _T. D. Noe_, Jun 18 2013 *)
%t A073214 Total/@Tuples[19^Range[0,10],2]//Union (* _Harvey P. Dale_, Jan 04 2019 *)
%o A073214 (Python)
%o A073214 from math import isqrt
%o A073214 def A073214(n): return 19**(a:=(k:=isqrt(m:=n<<1))+(m>k*(k+1))-1)+19**(n-1-(a*(a+1)>>1)) # _Chai Wah Wu_, Apr 09 2025
%Y A073214 Cf. A001029.
%Y A073214 Equals twice A073222.
%Y A073214 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), A073213 (17), A073215 (23).
%K A073214 easy,nonn,tabl
%O A073214 0,1
%A A073214 _Jeremy Gardiner_, Jul 20 2002