A103324 Square array T(n,k) read by antidiagonals: powers of Lucas numbers.

2, 4, 1, 8, 1, 3, 16, 1, 9, 4, 32, 1, 27, 16, 7, 64, 1, 81, 64, 49, 11, 128, 1, 243, 256, 343, 121, 18, 256, 1, 729, 1024, 2401, 1331, 324, 29, 512, 1, 2187, 4096, 16807, 14641, 5832, 841, 47, 1024, 1, 6561, 16384, 117649, 161051, 104976, 24389, 2209, 76

Offset

1,1

References

A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, identity 140.

Links

Table of n, a(n) for n=1..55.

Formula

T(n, k) = A000032(k)^n, n>=1, k>=0.

T(n, k) = Sum[i_1>=0, Sum[i_2>=0, ... Sum[i_{k-1}>=0, 2^i_1*C(n, i_1)*C(n-i_1, i_2)*C(n-i_2, i_3)*...*C(n-i_{k-2}, i_{k-1}) ] ... ]].

Example

2,1,3,4,7,11,18,
4,1,9,16,49,121,324,
8,1,27,64,343,1331,5832,
16,1,81,256,2401,14641,104976,
32,1,243,1024,16807,161051,1889568,
64,1,729,4096,117649,1771561,34012224,

Crossrefs

Rows include A000032, A001254, A075155, A099923, A103325.

Sequence in context: A127554 A182319 A204182 * A221073 A181266 A302192

Adjacent sequences: A103321 A103322 A103323 * A103325 A103326 A103327

Keyword

nonn,tabl

Author

Ralf Stephan, Feb 03 2005

Status

approved