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Search: id:A062938
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| A062938 |
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Squares of the form n(n+1)(n+2)(n+3) +1 = (n^2 +3n + 1)^2. |
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+0
9
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| 1, 25, 121, 361, 841, 1681, 3025, 5041, 7921, 11881, 17161, 24025, 32761, 43681, 57121, 73441, 93025, 116281, 143641, 175561, 212521, 255025, 303601, 358801, 421201, 491401, 570025, 657721, 755161, 863041, 982081, 1113025, 1256641
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) = product of first four terms of an arithmetic progression + n^4, where the first term is 1 and the common difference is n. E.g. a(1) = 1*2*3*4 +1^4 =25, a(4) = 1*5*9*13 + 4^4= 841 etc. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Sep 19 2003
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,1000
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FORMULA
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a(n+1)=Numerator of ((n + 2)! + (n - 2)!)/(n!) n=3,4,5,... - Artur Jasinski (grafix(AT)csl.pl), Jan 09 2007
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EXAMPLE
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2*3*4*5 + 1 = 121 = 11^2.
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MATHEMATICA
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Table[Numerator[((n + 2)! + (n - 2)!)/(n!)], {n, 3, 30}] - Artur Jasinski (grafix(AT)csl.pl), Jan 09 2007
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PROGRAM
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(PARI) j=[]; for(n=0, 70, j=concat(j, (n^2+3*n+1)^2)); j
(PARI) { for (n=0, 1000, write("b062938.txt", n, " ", (n^2 + 3*n + 1)^2) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 14 2009]
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CROSSREFS
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Sequence in context: A083509 A031151 A016970 this_sequence A141722 A090159 A025283
Adjacent sequences: A062935 A062936 A062937 this_sequence A062939 A062940 A062941
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 05 2001
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EXTENSIONS
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More terms from Jason Earls (zevi_35711(AT)yahoo.com), Harvey P. Dale (hpd1(AT)nyu.edu) and Dean Hickerson (dean.hickerson(AT)yahoo.com), Jul 06 2001
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