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A154560
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(n+3)^2*n/2 + 1.
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3
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1, 9, 26, 55, 99, 161, 244, 351, 485, 649, 846, 1079, 1351, 1665, 2024, 2431, 2889, 3401, 3970, 4599, 5291, 6049, 6876, 7775, 8749, 9801, 10934, 12151, 13455, 14849, 16336, 17919, 19601, 21385, 23274, 25271, 27379, 29601, 31940, 34399, 36981
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 8*a(n) is the y value of a solution (x, y) to the Diophantine equation 2*x^3+12*x^2 = y^2. The corresponding x value is A152811(n+1).
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index to sequences with linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
| G.f.: (1+5*x-4*x^2+x^3)/(1-x)^4.
a(n) = A058794(n)/2.
a(n) = A117560(n+2) - n - 1.
a(2*n) = A144129(n+1).
a(2*n-1) = A141530(n+1). a(n) = -a(-n-4). - Bruno Berselli, Sep 05 2011
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EXAMPLE
| a(5) = (5+3)^2*5/2+1 = 64*5/2+1 = 161.
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PROG
| (PARI) {for(n=0, 40, print1((n+3)^2*n/2+1, ", "))}
(MAGMA) [(n+3)^2*n/2 + 1: n in [0..50]]; // Vincenzo Librandi, Sep 06 2011
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CROSSREFS
| Cf. A058794 (row 3 of A007754), A117560 (n*(n^2-1)/2-1), A144129 (4*n^3-3*n), A141530, A152811 (2*(n^2+2*n-2)).
Sequence in context: A085367 A081267 A052153 * A048468 A048771 A055849
Adjacent sequences: A154557 A154558 A154559 * A154561 A154562 A154563
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KEYWORD
| nonn,easy
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AUTHOR
| Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 12 2009
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