A113153 Sum of the first n nonzero tribonacci numbers, in ascending order, as bases, with the same, in descending order, as exponents.

1, 2, 4, 8, 17, 54, 472, 27216, 84738887, 299164114847940, 311903053042108587337426568, 5846720173185251353387753850814872871131756204168

Offset: 1

Author

Jonathan Vos Post, Jan 04 2006

Keywords

• easy
• nonn

Examples

			For the tribonacci sequence starting t(1)=t(2)=1, t(3)=2, that is, the nonzero terms of A000073:
a(1) = t(1)^t(1) = 1^1 = 1.
a(2) = t(1)^t(2) + t(2)^t(1) = 1^1 + 1^1 = 2.
a(3) = t(1)^t(3) + t(2)^t(2) + t(3)^t(1) = 1^2 + 1^1 + 2^1 = 4.
a(4) = t(1)^t(4) + t(2)^t(3) + t(3)^t(2) + t(4)^t(1) = 1^4 + 1^2 + 2^1 + 4^1 = 8.
a(5) = 1^7 + 1^4 + 2^2 + 4^1 + 7^1 = 17.
a(6) = 1^13 + 1^7 + 2^4 + 4^2 + 7^1 + 13^1 = 54.
		

Crossrefs

Cf. A000073.

Programs

Mathematica

a[0] = a[1] = 0 ; a[2] = 1; a[n_] := a[n] = a[n - 1] + a[n - 2] + a[n - 3]; Table[Sum[a[k + 2]^(a[n - k + 1]), {k, 1, n}], {n, 1, 10}] (* G. C. Greubel, May 18 2017 *)

Formula

a(n) = Sum_{i=1..n} A000073(i+1)^A000073(n-i+2).

Extensions

Name clarified by Arthur O'Dwyer, Jul 24 2024