• Corpus ID: 16579563

Generating Functions, Weighted and Non-Weighted Sums for Powers of Second-Order Recurrence Sequences

@inproceedings{Stanica2000GeneratingFW,
  title={Generating Functions, Weighted and Non-Weighted Sums for Powers of Second-Order Recurrence Sequences},
  author={Pantelimon St{\`u}anic{\`u}a},
  year={2000}
}
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References

SHOWING 1-10 OF 11 REFERENCES

Generating functions for powers of Fibonacci numbers

Generating functions for powers of certain sequences of numbers

Partial Sums for Second-Order Recurrence Sequences

  • Fibonacci Quarterly,
  • 1994

Fibonacci and Lucas Numbers and the Golden Section

Generating functions for powers of a certain generalized sequence of numbers, Duke Math

  • J
  • 1965

Relations between a Sequence of Fibonacci Type and a Sequence of its Partial Sums

  • The Fibonacci Quarterly,
  • 1971

Primrose, Relations between a Sequence of Fibonacci Type and a Sequence of its Partial Sums, The Fibonacci Quarterly

  • Primrose, Relations between a Sequence of Fibonacci Type and a Sequence of its Partial Sums, The Fibonacci Quarterly
  • 1971

AMS Classification Numbers: 11B37,11B39, 05A10

  • AMS Classification Numbers: 11B37,11B39, 05A10
  • 2000

Generating Function for Powers of a Certain Generalized Sequence of Numbers.

  • Duke Math. J
  • 1965