A113154 Sum of the first n Lucas numbers, in ascending order, as bases, with the same, in descending order, as exponents.

1, 4, 32, 153, 2798, 197282, 392458839, 68701093784946, 26589104218033177611804, 1824800382950333667240931155126914915, 48519278097695351677170017554626182187607010493656860644716

Offset

1,2

Links

Table of n, a(n) for n=1..11.

Formula

a(n) = Sum_{i=1..n} (A000204(i))^A000204(n-i+1).

Example

For the Lucas sequence, starting L(1)=1, L(2)=3:
a(1) = L(1)^L(1) = 1^1 = 1.
a(2) = L(1)^L(2) + L(2)^L(1) = 1^3 + 3^1 = 4.
a(3) = L(1)^L(3) + L(2)^L(2) + L(3)^L(1) = 1^4 + 3^3 + 4^1 = 32.
a(4) = L(1)^L(4) + L(2)^L(3) + L(3)^L(2) + L(4)^L(1) = 1^7 + 3^4 + 4^3 + 7^1 = 153.
a(5) = 1^11 + 3^7 + 4^4 + 7^3 + 11^1 = 2798.
a(6) = 1^18 + 3^11 + 4^7 + 7^4 + 11^3 + 18^1 = 197282.
a(7) = 1^29 + 3^18 + 4^11 + 7^7 + 11^4 + 18^3 + 29^1 = 392458839.
a(8) = 1^47 + 3^29 + 4^18 + 7^11 + 11^7 + 18^4 + 29^3 + 47^1 = 68701093784946.
a(9) = 1^76 + 3^47 + 4^29 + 7^18 + 11^11 + 18^7 + 29^4 + 47^3 + 76^1 = 26589104218033177611804.
a(10) = 1^123 + 3^76 + 4^47 + 7^29 + 11^18 + 18^11 + 29^7 + 47^4 + 76^3 + 123^1 = 1824800382950333667240931155126914915.
a(11) = 1^199 + 3^123 + 4^76 + 7^47 + 11^29 + 18^18 + 29^11 + 47^7 + 76^4 + 123^3 + 199^1 = 48519278097695351677170017554626182187607010493656860644716.

Mathematica

Table[Sum[LucasL[k, 1]^(LucasL[n - k + 1, 1]), {k, 1, n}], {n, 1, 10}] (* G. C. Greubel, May 18 2017 *)

Prog

(PARI) for(n=1, 10, print1(sum(k=1, n, (fibonacci(k+1)+fibonacci(k-1))^(fibonacci(n-k+2)+fibonacci(n-k))), ", ")) \\ G. C. Greubel, May 18 2017

Crossrefs

Cf. A000204.

Sequence in context: A332430 A302070 A302267 * A302966 A337367 A334323

Adjacent sequences: A113151 A113152 A113153 * A113155 A113156 A113157

Keyword

easy,nonn

Author

Jonathan Vos Post, Jan 05 2006

Status

approved