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A008233
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floor(n/4)*floor((n+1)/4)*floor((n+2)/4)*floor((n+3)/4).
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4
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0, 0, 0, 0, 1, 2, 4, 8, 16, 24, 36, 54, 81, 108, 144, 192, 256, 320, 400, 500, 625, 750, 900, 1080, 1296, 1512, 1764, 2058, 2401, 2744, 3136, 3584, 4096, 4608, 5184, 5832, 6561, 7290, 8100, 9000, 10000, 11000, 12100, 13310, 14641, 15972, 17424, 19008, 20736
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..3000
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FORMULA
| Let b(n) = A002620(n), the quarter-squares. Then this sequence is b(0)*b(0), b(0)*b(1), b(1)*b(1), b(1)*b(2), b(2)*b(2), b(2)*b(3), ...
a(n)= +2*a(n-1) -a(n-2) +3*a(n-4) -6*a(n-5) +3*a(n-6) -3*a(n-8) +6*a(n-9) -3*a(n-10) +a(n-12) -2*a(n-13) +a(n-14). G.f. -x^4*(1+x^6+x^2+2*x^3+x^4) / ( (1+x)^3*(x^2+1)^3*(x-1)^5 ). - R. J. Mathar, Feb 20 2011
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MATHEMATICA
| Table[Floor[n/4]*Floor[(n + 1)/4]*Floor[(n + 2)/4]*Floor[(n + 3)/4], {n, 0, 50}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 03 2006
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PROG
| (Haskell)
a008233 n = product $ map (`div` 4) [n..n+3]
-- Reinhard Zumkeller, Jun 08 2011
(MAGMA) [Floor(n/4)*Floor((n+1)/4)*Floor((n+2)/4)*Floor((n+3)/4): n in [0..50]]; // Vincenzo Librandi, Jun 09 2011
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CROSSREFS
| Sequence in context: A160158 A010072 A005943 * A031923 A138278 A089827
Adjacent sequences: A008230 A008231 A008232 * A008234 A008235 A008236
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 03 2006
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