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A131557
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Triangular numbers which are the sums of five consecutive triangular numbers.
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1
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55, 2485, 17020, 799480, 5479705, 257429395, 1764447310, 82891465030, 568146553435, 26690794309585, 182941425758080, 8594352876220660, 58906570947547645, 2767354935348742255, 18967732903684582930, 891079694829418784770, 6107551088415488155135
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 1..250
Index to sequences with linear recurrences with constant coefficients, signature (1,322,-322,-1,1).
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FORMULA
| 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.
G.f.: -5*x*(11+486*x-635*x^2+2*x^4) / ( (x-1)*(x^2+18*x+1)*(x^2-18*x+1) ).
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EXAMPLE
| a(1) = 55=3+6+10+15+21.
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MAPLE
| a:= n-> `if`(n<2, [0, 55][n+1], (<<0|1|0>, <0|0|1>, <1|-323|323>>^iquo(n-2, 2, 'r'). `if`(r=0, <<2485, 799480, 257429395>>, <<17020, 5479705, 1764447310>>))[1, 1]): seq (a(n), n=1..20) # Alois P. Heinz, Sep 25 2008, revised Dec 15 2011
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CROSSREFS
| Cf. A129803.
Sequence in context: A053113 A012048 A020536 * A119166 A027548 A144748
Adjacent sequences: A131554 A131555 A131556 * A131558 A131559 A131560
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KEYWORD
| nonn,easy
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AUTHOR
| Richard Choulet (richardchoulet(AT)yahoo.fr), Oct 06 2007
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EXTENSIONS
| More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 25 2008
Corrected a(6) and a(8), Harvey P. Dale, Oct 02 2011
a(10), a(12), a(14) corrected at suggestion of Harvey P. Dale by D. S. McNeil (mcneil(AT)hku.hk), Oct 02 2011
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