A113153 - OEIS

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

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..12.

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

Adjacent sequences: A113150 A113151 A113152 * A113154 A113155 A113156

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Jan 04 2006

EXTENSIONS

Name clarified by Arthur O'Dwyer, Jul 24 2024

STATUS

approved