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Search: id:A131557
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| A131557 |
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Triangular numbers which are the sums of five consecutive triangular numbers. |
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+0
2
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OFFSET
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1,1
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FORMULA
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The subsequences with odd indices and even indices satisfy the same recurrence relations : a(n+2)=322*a(n+1)-a(n)-680 and a(n+1)=161*a(n)-340+9*(320*a(n)^2-1360*a(n)-175)^0.5. The g.f. f(z)=a(1)*z+a(2)*z^2+... is given by (55*z+2485*z^2-745*z^3-3175*z^4+10*z^5+10*z^6)/((1-z^2)*(1-322*z^2+z^4)) ; we observe that the numerator is divisible by 1+z.
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EXAMPLE
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a(1)=55=3+6+10+15+21
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CROSSREFS
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Cf. A129803.
Adjacent sequences: A131554 A131555 A131556 this_sequence A131558 A131559 A131560
Sequence in context: A053113 A012048 A020536 this_sequence A119166 A027548 A076657
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KEYWORD
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nonn,easy,more
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AUTHOR
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Richard Choulet (richardchoulet(AT)yahoo.fr), Oct 06 2007
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