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A113153
Sum of the first n nonzero tribonacci numbers, in ascending order, as bases, with the same, in descending order, as exponents.
18
1, 2, 4, 8, 17, 54, 472, 27216, 84738887, 299164114847940, 311903053042108587337426568, 5846720173185251353387753850814872871131756204168
OFFSET
1,2
FORMULA
a(n) = Sum_{i=1..n} A000073(i+1)^A000073(n-i+2).
EXAMPLE
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.
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 *)
CROSSREFS
Cf. A000073.
Sequence in context: A364210 A231221 A231435 * A372543 A255999 A171719
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Jan 04 2006
EXTENSIONS
Name clarified by Arthur O'Dwyer, Jul 24 2024
STATUS
approved