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A113153 Sum of the first n 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

FORMULA

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

EXAMPLE

For the tribonacci sequence, starting t(1)=t(2)=1:

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.

a(7) = 1^24 + 1^13 + 2^7 + 4^4 + 7^2 + 13^1 + 24^1 = 472.

a(8) = 1^44 + 1^24 + 2^13 + 4^7 + 7^4 + 13^2 + 24^1 + 44^1 = 27216.

a(9) = 1^81 + 1^44 + 2^24 + 4^13 + 7^7 + 13^4 + 24^2 + 44^1 + 81^1 = 84738887.

a(10) = 1^149 + 1^81 + 2^44 + 4^24 + 7^13 + 13^7 + 24^4 + 44^2 + 81^1 + 149^1 = 299164114847940.

a(11) = 1^274 + 1^149 + 2^81 + 4^44 + 7^24 + 13^13 + 24^7 + 44^4 + 81^2 + 149^1 + 274^1 = 311903053042108587337426568.

a(12) = 1^504 + 1^274 + 2^149 + 4^81 + 7^44 + 13^24 + 24^13 + 44^7 + 81^4 + 149^2 + 274^1 + 504^1 = 5846720173185251353387753850814872871131756204168.

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: A283162 A231221 A231435 * A255999 A171719 A185178

Adjacent sequences:  A113150 A113151 A113152 * A113154 A113155 A113156

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Jan 04 2006

STATUS

approved

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Last modified February 25 16:14 EST 2018. Contains 299653 sequences. (Running on oeis4.)