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A023855
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a(n) = 1(n) + 2(n-1) + 3(n-2) + ... + (n+1-k)k, where k = floor((n+1)/2).
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4
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1, 2, 7, 10, 22, 28, 50, 60, 95, 110, 161, 182, 252, 280, 372, 408, 525, 570, 715, 770, 946, 1012, 1222, 1300, 1547, 1638, 1925, 2030, 2360, 2480, 2856, 2992, 3417, 3570, 4047, 4218, 4750, 4940, 5530, 5740, 6391, 6622, 7337, 7590, 8372, 8648, 9500, 9800, 10725, 11050
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Given a rectangle of perimeter 2*n one can form rectangles having this perimter for a number of different rectangles or squares depending on how large 2*n is. The sequence lists the total areas of all such rectangles for each 2*n. [J. M. Bergot, Sep 14 2011]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index to sequences with linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1)
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FORMULA
| a(n) = (n+1)*(n+3)*(2*n+1)/24 if n is odd, or n*(n+1)*(n+2)/12 if n is even
G.f.: [x(1+x+2x^2)]/[(1-x)^4(1+x)^3]. - Ralf Stephan, Apr 28 2004
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MATHEMATICA
| LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {1, 2, 7, 10, 22, 28, 50}, 50] (* Vincenzo Librandi, Jan 23 2012 *)
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PROG
| (PARI) a(n)=if(n%2, (n+1)*(n+3)*(2*n+1)/24, n*(n+1)*(n+2)/12)
(Haskell)
a023855 n = sum $ zipWith (*) [1 .. div (n+1) 2] [n, n-1 ..]
-- Reinhard Zumkeller, Jan 23 2012
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CROSSREFS
| (Conjecture) Antidiagonal sums of triangle A075462. - L. Edson Jeffery, Jan 20 2012
Sequence in context: A155171 A049830 A022302 * A191832 A066964 A066967
Adjacent sequences: A023852 A023853 A023854 * A023856 A023857 A023858
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KEYWORD
| nonn,easy
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
| Formula, program, and slight revision by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Feb 23 2010
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