login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A103324 Square array T(n,k) read by antidiagonals: powers of Lucas numbers. 6
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 (list; table; graph; refs; listen; history; text; internal format)
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 A087060

Adjacent sequences:  A103321 A103322 A103323 * A103325 A103326 A103327

KEYWORD

nonn,tabl

AUTHOR

Ralf Stephan, Feb 03 2005

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified January 22 08:43 EST 2018. Contains 298042 sequences.