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A051868 16-gonal (or hexadecagonal) numbers: a(n) = n*(7*n-6). 8

%I

%S 0,1,16,45,88,145,216,301,400,513,640,781,936,1105,1288,1485,1696,

%T 1921,2160,2413,2680,2961,3256,3565,3888,4225,4576,4941,5320,5713,

%U 6120,6541,6976,7425,7888,8365,8856,9361,9880,10413,10960,11521

%N 16-gonal (or hexadecagonal) numbers: a(n) = n*(7*n-6).

%C Sequence found by reading the line from 0, in the direction 0, 16, ... and the parallel line from 1, in the direction 1, 45, ..., in the square spiral whose vertices are the generalized 16-gonal numbers. - _Omar E. Pol_, Jul 18 2012

%C This is also a star octagonal number: a(n) = A000567(n) + 8*A000217(n-1). - _Luciano Ancora_, Mar 29 2015

%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 189.

%D E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 6.

%H Ivan Panchenko, <a href="/A051868/b051868.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = 14*n + a(n-1) - 13, with n>0, a(0)=0. - _Vincenzo Librandi_, Aug 06 2010

%F G.f.: x*(1+13*x)/(1-x)^3. - _Bruno Berselli_, Feb 04 2011

%F a(0)=0, a(1)=1, a(2)=16; for n>2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Harvey P. Dale_, May 07 2011

%F a(14*a(n) + 92*n + 1) = a(14*a(n) + 92*n) + a(14*n+1). - _Vladimir Shevelev_, Jan 24 2014

%p a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=2*a[n-1]-a[n-2]+14 od: seq(a[n], n=0..41); # _Zerinvary Lajos_, Feb 18 2008

%t s=0;lst={s};Do[s+=n++ +1;AppendTo[lst, s], {n, 0, 6!, 14}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 16 2008 *)

%t Table[n(7n-6),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,1,16}, 51] (* _Harvey P. Dale_, May 07 2011 *)

%o (PARI) a(n)=n*(7*n-6) \\ _Charles R Greathouse IV_, Jan 24 2014

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, Dec 15 1999

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Last modified November 14 17:24 EST 2019. Contains 329126 sequences. (Running on oeis4.)