A304780 Consider a triangle whose first row is {1,2} and, for n > 1, has as its n-th row the integers k through 2k where k is the sum of the numbers in the (n-1)th row. Then a(n) is the first number in the n-th row.

1, 3, 18, 513, 395523, 234658258578, 82596747478641253260993, 10233334041075645341729789249315281196742910563, 157081688394356396673208173772909833928515988895188885472258972148661958252271815996039831298

Offset: 1

Author

Nathaniel J. Strout, May 18 2018

Keywords

• nonn

Examples

			Triangle begins:
  1, 2; (row sum = 3)
  3, 4, 5, 6; (row sum = 18)
  18, 19, 20, 21, ... 33, 34, 35, 36; (row sum = 513)
  513, 514, 515, 516, ..., 1023, 1024, 1025, 1026;
  ...
		

Crossrefs

Cf. A000217.

Programs

Mathematica

RecurrenceTable[{a[1] == 1, a[n] == (3*a[n-1]*(a[n-1] + 1))/2}, a, {n, 1, 10}] (* Vaclav Kotesovec, Jul 23 2018 *)
Nest[Append[#, Range[#, 2 #] &@ Total@ Last@ #] &, {{1, 2}}, 3] // Flatten (* Michael De Vlieger, Jul 26 2018 *)

PARI

a(n) = if (n==1, 1, (3*a(n - 1)*(a(n - 1) + 1))/2); \\ Michel Marcus, May 24 2018

Formula

a(1) = 1, a(n) = (3*a(n-1)*(a(n-1) + 1))/2 for n > 1.

a(n) ~ (2/3) * c^(2^n), where c = 1.515006464529590220430714781603262955960312205695360166833... - Vaclav Kotesovec, Jul 23 2018