THE NUMBER OF REPRESENTATIONS OF AN INTEGER AS A SUM INVOLVING GENERALIZED PENTAGONAL NUMBERS
2012 ◽
Vol 08
(04)
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pp. 1041-1056
Keyword(s):
In this paper, using the (p, k)-parametrization of theta functions given by Alaca, Alaca and Williams, we establish some theta function identities. From these identities, we obtain some formulas for the number of representations of a natural number as a sum of quadratic polynomials involving generalized pentagonal numbers. In particular, we derive a formula for the number of representations of a natural number as a sum of twelve generalized pentagonal numbers.
2012 ◽
Vol 6
(1)
◽
pp. 114-125
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2012 ◽
Vol 08
(08)
◽
pp. 1977-2002
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2008 ◽
Vol 04
(03)
◽
pp. 461-474
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2016 ◽
Vol 12
(04)
◽
pp. 945-954
2012 ◽
Vol 09
(01)
◽
pp. 189-204
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Keyword(s):
2018 ◽
Vol 11
(1)
◽
pp. 1
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Keyword(s):
2020 ◽
Vol 9
(7)
◽
pp. 4929-4936