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A032438
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n^2-floor( (n+1)/2 )^2.
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3
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0, 0, 3, 5, 12, 16, 27, 33, 48, 56, 75, 85, 108, 120, 147, 161, 192, 208, 243, 261, 300, 320, 363, 385, 432, 456, 507, 533, 588, 616, 675, 705, 768, 800, 867, 901, 972, 1008, 1083, 1121, 1200, 1240, 1323, 1365
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| The answer to a question from Mike and Laurie Crain (2crains(AT)concentric.net): how many even numbers are there in an n X n multiplication table starting at 1X1?
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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 (1,2,-2,-1,1).
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FORMULA
| G.f.: x^2*(x^2+2*x+3)/(1-x^2)^2/(1-x). - Ralf Stephan, Jun 10 2003
a(n) = (1/8)*(2*n*(3*n-1)+(2*n+1)*(-1)^n-1). a(-n-1) = A014255(n). - Bruno Berselli, Sep 27 2011
a(0)=0, a(1)=0, a(2)=3, a(3)=5, a(4)=12, a(n)=a(n-1)+2*a(n-2)- 2*a(n-3)- a(n-4)+a(n-5) [From Harvey P. Dale, Nov 24 2011]
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MATHEMATICA
| Table[n^2-Floor[((n+1)/2)]^2, {n, 0, 50}] (* or *) LinearRecurrence[ {1, 2, -2, -1, 1}, {0, 0, 3, 5, 12}, 51]
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PROG
| (MAGMA) [n^2-Floor( (n+1)/2 )^2 : n in [0..60]]; // Vincenzo Librandi, Sep 27 2011
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CROSSREFS
| First differences are in A059029.
Sequence in context: A080560 A151866 A057587 * A025083 A203150 A126471
Adjacent sequences: A032435 A032436 A032437 * A032439 A032440 A032441
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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