A073214 Sum of two powers of 19.

2, 20, 38, 362, 380, 722, 6860, 6878, 7220, 13718, 130322, 130340, 130682, 137180, 260642, 2476100, 2476118, 2476460, 2482958, 2606420, 4952198, 47045882, 47045900, 47046242, 47052740, 47176202, 49521980, 94091762, 893871740, 893871758, 893872100, 893878598, 894002060, 896347838, 940917620, 1787743478

Offset: 0

Author

Jeremy Gardiner, Jul 20 2002

Keywords

• easy
• nonn
• tabl

Examples

			T(2,0) = 19^2 + 19^0 = 362.
Table begins:
       2;
      20,     38;
     362,    380,    722;
    6860,   6878,   7220,  13718;
  130322, 130340, 130682, 137180, 260642;
  ...
		

Links

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

Crossrefs

Cf. A001029.

Equals twice A073222.

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).

Programs

Mathematica

Flatten[Table[Table[19^n + 19^m, {m, 0, n}], {n, 0, 7}]] (* T. D. Noe, Jun 18 2013 *)
Total/@Tuples[19^Range[0,10],2]//Union (* Harvey P. Dale, Jan 04 2019 *)

Python

from math import isqrt
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

Formula

T(n,m) = 19^n + 19^m for n >= 0 and m in [0..n].

Bivariate g.f.: (2 - 20*x) / ((1 - x) * (1 - 19*x) * (1 - 19*x*y)). - J. Douglas Morrison, Jul 28 2021