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A069074
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(2*n+2)*(2*n+3)*(2*n+4) = 24*A000330(n+1).
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4
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24, 120, 336, 720, 1320, 2184, 3360, 4896, 6840, 9240, 12144, 15600, 19656, 24360, 29760, 35904, 42840, 50616, 59280, 68880, 79464, 91080, 103776, 117600, 132600, 148824, 166320, 185136, 205320, 226920, 249984, 274560, 300696, 328440, 357840
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| sqrt(sum{x=0..n: 2*a(x)} + 1) = A056220(n+2) [From Doug Bell (bell.doug(AT)gmail.com), Mar 09 2009]
Second leg of Pythagorean triangles with hypotenuse a square: A057769(n)^2 + a(n-1)^2 = A007204(n)^2. -- [Martin Renner, Nov 12 2011]
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REFERENCES
| Albert H. Beiler, Recreations in the theory of numbers, New York: Dover, (2nd ed.) 1966, p. 106, table 53.
T. J. I'a. Bromwich, Introduction to the Theory of Infinite Series, Macmillan, 2nd. ed. 1949, p. 190.
Jolley, Summation of Series, Dover (1961).
Konrad Knopp, Theory and application of infinite series, Dover, p. 269
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Konrad Knopp, Theorie und Anwendung der unendlichen Reihen, Berlin, J. Springer, 1922. (Original german edition of "Theory and Application of Infinite Series")
Index to sequences with linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
| sum(n=0, inf, (-1)^n/a(n))=(Pi-3)/4 = 0.03539816339.. [Jolley eq 244]
sum(n=0..infinity) 1/a(n) = 3/4-log(2) = 0.05685281.. [Jolley eq.249]
G.f. ( 24+24*x ) / (x-1)^4 . - R. J. Mathar, Oct 03 2011
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PROG
| (MAGMA) [(2*n+2)*(2*n+3)*(2*n+4): n in [0..40]]; // Vincenzo Librandi, Oct 04 2011
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CROSSREFS
| Cf. A001844. A001844(n+1)^2 - a(n) and A001844(n+1)^2 + a(n) are both square numbers. [From Doug Bell (bell.doug(AT)gmail.com), Mar 08 2009]
Cf. A000466. a(n) = sum{k=0..2n+3: A000466(n+1) + 2k} which is the sum of 2n+4 consecutive odd integers starting at A000466(n+1). [From Doug Bell (bell.doug(AT)gmail.com), Mar 08 2009]
Sequence in context: A137799 A198438 A114200 * A059775 A052762 A099317
Adjacent sequences: A069071 A069072 A069073 * A069075 A069076 A069077
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KEYWORD
| easy,nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 05 2002
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