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A172118
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n*(n+1)*(5*n^2-n-3)/2.
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0
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0, 1, 45, 234, 730, 1755, 3591, 6580, 11124, 17685, 26785, 39006, 54990, 75439, 101115, 132840, 171496, 218025, 273429, 338770, 415170, 503811, 605935, 722844, 855900, 1006525, 1176201, 1366470, 1578934, 1815255, 2077155, 2366416, 2684880
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OFFSET
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0,3
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COMMENTS
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Numbers: 0,1,2,3,4,5,6,7,8,9,10,.. and A172117: 0,1,23,86,210,..
45 is in the sequence because 45=23*2-(1+0); 234=86*3-(23+1+0); 730=210*4-(86+23+1+0)
a(n) = n*(n*(n+1)*(20*n-17)/6) - sum[i*(i+1)*(20*i-17)/2, i=0..n-1] = n*(n+1)*(5*n^2-n-3)/2. More generally: n*(n*(n+1)*(2*d*n-2*d+3)/6)-sum[i*(i+1)*(2*d*i-2*d+3)/6, i=0..n-1] = n*(n+1)*(3*d*n^2-d*n+4*n-2*d+2)/12; in this sequence is d=10. - Bruno Berselli, May 07 2010
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LINKS
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Table of n, a(n) for n=0..32.
Index to sequences with linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
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FORMULA
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G.f. -x*(1+40*x+19*x^2) / (x-1)^5 . - R. J. Mathar, Nov 17 2011
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CROSSREFS
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Cf. A172117
Sequence in context: A203835 A087442 A169717 * A127073 A089549 A178540
Adjacent sequences: A172115 A172116 A172117 * A172119 A172120 A172121
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, Jan 26 2010
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EXTENSIONS
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Simplified formula and corrected sequence A172117 by Bruno Berselli, May 07 2010
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STATUS
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approved
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