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A056520
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(n+2)*(2*n^2-n+3)/6.
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12
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1, 2, 6, 15, 31, 56, 92, 141, 205, 286, 386, 507, 651, 820, 1016, 1241, 1497, 1786, 2110, 2471, 2871, 3312, 3796, 4325, 4901, 5526, 6202, 6931, 7715, 8556, 9456, 10417, 11441, 12530, 13686, 14911, 16207, 17576, 19020, 20541, 22141, 23822
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n) = A000330(n)+1.
Hankel transform of A030238. - Paul Barry, Oct 16 2007
Equals (1, 2, 3, 4, 5,...) convolved with (1, 0, 3, 5, 7, 9,...). [From Gary W. Adamson, Jul 31 2010]
a(n) equals n!^2 times the determinant of the n X n matrix whose (i,j)-entry is 1 + KroneckerDelta[i, j] (-1 + (1 + i^2)/i^2). - John M. Campbell, May 20, 2011
Let b(0)=b(1)=1, b(n)=max(b(n-1)+(n-1)^2,b(n-2)+(n-2)^2); then A056520(n)=b(n+1); [Yalcin Aktar, Jul 28 2011]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Guo-Niu Han, Enumeration of Standard Puzzles
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FORMULA
| a(n) = a(n-1)+n^2.
G.f.: (1-2*x+4*x^2-x^3)/(1-x)^4. [From Paul Barry, Apr 14 2010]
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MATHEMATICA
| a[n_] := (n+2)*(2*n^2-n+3)/6; Table[a[n], {n, 0, 100}] [From Vladimir Orlovsky, Dec 17 2008]
s = 1; lst = {s}; Do[s += n^2; AppendTo[lst, s], {n, 1, 41, 1}]; lst [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 12 2009]
Table[n!^2*Det[Array[KroneckerDelta[#1, #2](((#1^2+1)/(#1^2))-1)+1&, {n, n}]], {n, 1, 20}] - John M. Campbell, May 20, 2011
FoldList[#1 + #2^2 &, 1, Range@ 40] (* Robert G. Wilson v, 28 Oct 2011 *)
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PROG
| (MAGMA)[(n+2)*(2*n^2-n+3)/6: n in [0..40]]; // Vincenzo Librandi, May 24 2011
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CROSSREFS
| Sequence in context: A098651 A087427 A141126 * A078406 A101352 A192980
Adjacent sequences: A056517 A056518 A056519 * A056521 A056522 A056523
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Laura Kasavan (maui12129(AT)cswebmail.com), Aug 26 2000
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