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A059859
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Sum of squares of first n quarter-squares (A002620).
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2
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0, 0, 1, 5, 21, 57, 138, 282, 538, 938, 1563, 2463, 3759, 5523, 7924, 11060, 15156, 20340, 26901, 35001, 45001, 57101, 71742, 89166, 109902, 134238, 162799, 195923, 234339, 278439, 329064, 386664, 452200, 526184, 609705, 703341
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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FORMULA
| If n even a(n) = n*(n+2)*(2*n^3+n^2-2*n+4)/160, if n odd a(n) = (n^2-1)*(2*n^3+5*n^2+2*n-5)/160.
a(n)= 3*a(n-1) -8*a(n-3) +6*a(n-4) +6*a(n-5) -8*a(n-6) +3*a(n-8) -a(n-9). G.f.: x^2*(1+2*x+6*x^2+2*x^3+x^4)/((1+x)^3 * (x-1)^6). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 15 2010]
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MAPLE
| A059859 := n->add(A002620(i)^2, i=0..n);
f1 := n->1/160*(n-1)*(1+n)*(2*n^3+5*n^2+2*n-5); f2 := n->1/160*n*(n+2)*(2*n^3+n^2-2*n+4); A059859 := n-> if n mod 2 = 0 then f2(n) else f1(n); fi;
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CROSSREFS
| Cf. A002620.
Sequence in context: A146854 A033275 A166464 * A146617 A203233 A112561
Adjacent sequences: A059856 A059857 A059858 * A059860 A059861 A059862
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Feb 26 2001
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