Journal of Integer Sequences, Vol. 16 (2013), Article 13.5.7

Some Number Arrays Related to Pascal and Lucas Triangles

Claudio de J. Pita Ruiz V.
Universidad Panamericana
Mexico City


By taking repeated convolutions of the sequence np with the constant sequence 1, we form the number arrays of the coefficients resulting when we write the mentioned convolutions as linear combinations of certain binomial coefficients. According to this procedure, Pascal and Lucas triangles correspond to the cases p = 1 and p = 2 respectively. We show that these arrays have some properties similar to the well-known properties of Pascal and Lucas triangles.

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(Concerned with sequences A000012 A000027 A000051 A000217 A000290 A000292 A000330 A000537 A000538 A000578 A000583 A000670 A001550 A001551 A001552 A002415 A003215 A005408 A005914 A005917 A008277 A008588 A024166 A050946 A101089 A101103.)

Received February 25 2013; revised version received May 14 2013. Published in Journal of Integer Sequences, June 4 2013.

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