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A131479
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a(n) = floor(n^4/4).
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3
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0, 0, 4, 20, 64, 156, 324, 600, 1024, 1640, 2500, 3660, 5184, 7140, 9604, 12656, 16384, 20880, 26244, 32580, 40000, 48620, 58564, 69960, 82944, 97656, 114244, 132860, 153664, 176820, 202500, 230880, 262144, 296480, 334084, 375156
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OFFSET
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0,3
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
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FORMULA
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From R. J. Mathar, Dec 19 2008: (Start)
G.f.: 4*x^2*(1+x+x^2)/((1+x)*(1-x)^5).
a(n) = 4*A011863(n-1). (End)
a(n) = floor(n^2/2)*ceiling(n^2/2) = A007590(n) * A000982(n). - Enrique Pérez Herrero, May 31 2015
Sum_{n>=2} 1/a(n) = Sum_{n>=1} 1/(4n^4) + Sum_{n>=1} 1/(2n*(n+1)*(2n^2+2n+1)) = Zeta(4)/4 + (3-Pi*tanh(Pi/2))/2. - Enrique Pérez Herrero, May 31 2015
a(2*k) = 4*k^4; a(2*k+1) = 2*(k^3*(k+1) + k*(k+1)^3). - Robert Israel, Jun 01 2015
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MAPLE
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seq(op([4*k^4, 2*(k^3*(k+1)+k*(k+1)^3)]), k=0..100); # Robert Israel, Jun 01 2015
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MATHEMATICA
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Table[Floor[n^4/4], {n, 0, 20}] (* Enrique Pérez Herrero, May 31 2015 *)
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PROG
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(MAGMA) [Floor(n^4/4): n in [0..60]]; // Vincenzo Librandi, Jun 16 2011
(PARI) vector(50, n, n--; n^4\4) \\ Michel Marcus, Jun 02 2015
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CROSSREFS
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Cf. A000982, A008619, A004526, A007590, A036487.
Cf. A131478.
Sequence in context: A169638 A226424 A225260 * A194094 A055538 A302317
Adjacent sequences: A131476 A131477 A131478 * A131480 A131481 A131482
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KEYWORD
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nonn
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AUTHOR
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Mohammad K. Azarian, Jul 27 2007
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STATUS
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approved
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