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A056520 (n+2)*(2*n^2-n+3)/6. 19

%I

%S 1,2,6,15,31,56,92,141,205,286,386,507,651,820,1016,1241,1497,1786,

%T 2110,2471,2871,3312,3796,4325,4901,5526,6202,6931,7715,8556,9456,

%U 10417,11441,12530,13686,14911,16207,17576,19020,20541,22141,23822

%N (n+2)*(2*n^2-n+3)/6.

%C a(n) = A000330(n)+1.

%C Hankel transform of A030238. - _Paul Barry_, Oct 16 2007

%C Equals (1, 2, 3, 4, 5,...) convolved with (1, 0, 3, 5, 7, 9,...). - _Gary W. Adamson_, Jul 31 2010

%C 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

%C 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

%C Positions of ones in A253903. - _Harvey P. Dale_, Mar 05 2015

%H Vincenzo Librandi, <a href="/A056520/b056520.txt">Table of n, a(n) for n = 0..1000</a>

%H Guo-Niu Han, <a href="http://www-irma.u-strasbg.fr/~guoniu/papers/p77puzzle.pdf">Enumeration of Standard Puzzles</a>\Guo-Niu Han, <a href="/A196265/a196265.pdf">Enumeration of Standard Puzzles</a> [Cached copy]

%H Amit Kumar Singh, Akash Kumar and Thambipillai Srikanthan, <a href="http://www.ece.nus.edu.sg/stfpage/eleak/pdf/akumar_todaes_2012.pdf">Accelerating Throughput-aware Run-time Mapping for Heterogeneous MPSoCs</a>, ACM Transactions on Design Automation of Electronic Systems, 2012. - From _N. J. A. Sloane_, Dec 25 2012

%F a(n) = a(n-1)+n^2.

%F G.f.: (1-2*x+4*x^2-x^3)/(1-x)^4. - _Paul Barry_, Apr 14 2010

%t a[n_] := (n+2)*(2*n^2-n+3)/6; Table[a[n], {n, 0, 100}] (* _Vladimir Joseph Stephan Orlovsky_, Dec 17 2008 *)

%t s = 1; lst = {s}; Do[s += n^2; AppendTo[lst, s], {n, 1, 41, 1}]; lst (* _Zerinvary Lajos_, Jul 12 2009 *)

%t 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 *)

%t FoldList[#1 + #2^2 &, 1, Range@ 40] (* _Robert G. Wilson v_, Oct 28 2011 *)

%o (MAGMA)[(n+2)*(2*n^2-n+3)/6: n in [0..40]]; // _Vincenzo Librandi_, May 24 2011

%o (PARI) a(n)=(n+2)*(2*n^2-n+3)/6 \\ _Charles R Greathouse IV_, Jul 02 2013

%Y Cf. A253903.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Laura Kasavan (maui12129(AT)cswebmail.com), Aug 26 2000

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Last modified July 21 04:40 EDT 2019. Contains 325189 sequences. (Running on oeis4.)