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In my work on number of partitions of natural numbers in parts non greater than 5 arise the sequence $$775,1015,1285,1585,1915,2275,2665,3085,3535,4015,4525,5065,5635,6235,6865,7525,8215,8935,9685$$ I now first 60 terms of this sequence and all can be divided by 5. Any help on general term.

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Could you explain how, precisely, you obtained the number $775$? It obviously isn't the number of ways of partitioning $1$ into parts of size at most $5$... –  Zhen Lin Aug 7 '11 at 12:16
    
775 is first term of an additional sequence that arise in context. –  Adi Dani Aug 7 '11 at 12:24

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up vote 5 down vote accepted

Hint: Consider the corresponding sequence of differences: $240,270,300,330,\ldots$.

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Using this hint you can find that $a_n = 5(3n^2 + 39n + 113)$, $n \geq 1$. –  Shai Covo Aug 7 '11 at 13:01

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