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Search: id:A103324
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| A103324 |
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Square array T(n,k) read by antidiagonals: powers of Lucas numbers. |
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+0
7
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| 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; listen)
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OFFSET
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1,1
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REFERENCES
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A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, identity 140.
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FORMULA
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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}) ] ... ]].
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EXAMPLE
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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,
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CROSSREFS
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Rows include A000032, A001254, A075155, A099923, A103325.
Sequence in context: A112852 A121531 A127554 this_sequence A087060 A065278 A112931
Adjacent sequences: A103321 A103322 A103323 this_sequence A103325 A103326 A103327
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KEYWORD
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nonn,tabl
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AUTHOR
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Ralf Stephan, Feb 03 2005
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