A059403 Quarter-squared applied twice.
0, 0, 0, 1, 4, 9, 20, 36, 64, 100, 156, 225, 324, 441, 600, 784, 1024, 1296, 1640, 2025, 2500, 3025, 3660, 4356, 5184, 6084, 7140, 8281, 9604, 11025, 12656, 14400, 16384, 18496, 20880, 23409, 26244, 29241, 32580, 36100, 40000, 44100, 48620, 53361, 58564, 64009
Offset: 0
Examples
a(9)=100 since the ninth quarter-square is 20 and the twentieth quarter-square is 100.
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..1000 (first 501 terms from Harry J. Smith)
- Index entries for linear recurrences with constant coefficients, signature (2, 1, -4, 2, 0, -2, 4, -1, -2, 1).
Crossrefs
Cf. A008233 for an alternative approach.
Programs
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Mathematica
Floor[Floor[Range[0,50]^2/4]^2/4] (* or *) LinearRecurrence[{2,1,-4,2,0,-2,4,-1,-2,1},{0,0,0,1,4,9,20,36,64,100},50] (* Harvey P. Dale, Dec 13 2014 *) -
PARI
a(n) = { (n^2\4)^2\4 } \\ Harry J. Smith, Jun 26 2009
Formula
a(4*n) = 4n^4; a(4*n+1) = n^2*(2*n+1)^2;
a(4*n+2) = 2*n*(n+1)*(2*n*(n+1)+1); a(4*n+3) = (n+1)^2*(2*n+1)^2.
G.f.: x^3*(1 + 2*x + 2*x^3 + x^4)/((1 - x)^5*(1 + x)^3*(1 + x^2)). - R. J. Mathar, Sep 09 2008