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%I #23 Jan 05 2025 19:51:41
%S 0,1,2,5,12,70
%N Generalized pentagonal numbers that are also Pell numbers.
%C Intersection of A000129 and A001318.
%C Except for 0 and 2, these are also ordinary pentagonal numbers.
%C All terms are shown, as confirmed by Siva Rama Prasad and Srinivasa Rao (2002).
%C All (generalized) g-gonal numbers in the Pell sequence up to g=20 have been determined, see Tengely (2009).
%H V. Sima Rama Prasad and B. Srinivasa Rao, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/40-3/prasad.pdf">Pentagonal Numbers in the Pell Sequence and Diophantine Equations 2x^2=y^2(3y-1)^2+-2</a>, The Fibonacci Quarterly, Vol. 40, No. 3 (2002), 233-241.
%H Szabolcs Tengely, <a href="http://shrek.unideb.hu/~tengely/G-gonal-FQ.pdf">Finding g-gonal numbers in recurrence sequences</a>, Fibonacci Quarterly, vol.46/47, No. 3 (2009), 235-240.
%Y Cf. A000129, A001318.
%Y Cf. A039595, A248506, A292851.
%K nonn,fini,easy,full
%O 0,3
%A _Tomohiro Yamada_, Sep 29 2017