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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
1
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| 55, 2485, 17020, 799480, 5479705, 257429385, 1764447310, 82891461800, 568146553435, 26690793269525, 182941425758080, 8594352541324560, 58906570947547645, 2767354827513238105, 18967732903684582930
(list; graph; listen)
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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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MAPLE
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a:= n-> (Matrix([[2485, 55, 0, 10, -3175, 2485]]). Matrix (6, (i, j)-> if i=j-1 then 1 elif j=1 then [0, 323, 0, -323, 0, 1][i] else 0 fi)^n)[1, 3]: seq (a(n), n=1..20); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 25 2008]
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CROSSREFS
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Cf. A129803.
Sequence in context: A053113 A012048 A020536 this_sequence A119166 A027548 A144748
Adjacent sequences: A131554 A131555 A131556 this_sequence A131558 A131559 A131560
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KEYWORD
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nonn,easy
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AUTHOR
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Richard Choulet (richardchoulet(AT)yahoo.fr), Oct 06 2007
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EXTENSIONS
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More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 25 2008
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