A293023 Generalized pentagonal numbers that are also Pell numbers.

0, 1, 2, 5, 12, 70

Offset: 0

Author

Tomohiro Yamada, Sep 29 2017

Keywords

• nonn
• fini
• easy
• full

Comments

Intersection of A000129 and A001318.

Except for 0 and 2, these are also ordinary pentagonal numbers.

All terms are shown, as confirmed by Siva Rama Prasad and Srinivasa Rao (2002).

All (generalized) g-gonal numbers in the Pell sequence up to g=20 have been determined, see Tengely (2009).

Links

• V. Sima Rama Prasad and B. Srinivasa Rao, Pentagonal Numbers in the Pell Sequence and Diophantine Equations 2x^2=y^2(3y-1)^2+-2, The Fibonacci Quarterly, Vol. 40, No. 3 (2002), 233-241.
• Szabolcs Tengely, Finding g-gonal numbers in recurrence sequences, Fibonacci Quarterly, vol.46/47, No. 3 (2009), 235-240.

Crossrefs

Cf. A000129, A001318.

Cf. A039595, A248506, A292851.