A113153 Sum of the first n 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

1,2

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: A364210 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