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 A051868 16-gonal (or hexadecagonal) numbers: a(n) = n*(7*n-6). 8
 0, 1, 16, 45, 88, 145, 216, 301, 400, 513, 640, 781, 936, 1105, 1288, 1485, 1696, 1921, 2160, 2413, 2680, 2961, 3256, 3565, 3888, 4225, 4576, 4941, 5320, 5713, 6120, 6541, 6976, 7425, 7888, 8365, 8856, 9361, 9880, 10413, 10960, 11521 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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 This is also a star octagonal number: a(n) = A000567(n) + 8*A000217(n-1). - Luciano Ancora, Mar 29 2015 REFERENCES A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 189. E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 6. LINKS Ivan Panchenko, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = 14*n + a(n-1) - 13, with n>0, a(0)=0. - Vincenzo Librandi, Aug 06 2010 G.f.: x*(1+13*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011 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 a(14*a(n) + 92*n + 1) = a(14*a(n) + 92*n) + a(14*n+1). - Vladimir Shevelev, Jan 24 2014 MAPLE 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 MATHEMATICA s=0; lst={s}; Do[s+=n++ +1; AppendTo[lst, s], {n, 0, 6!, 14}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 16 2008 *) Table[n(7n-6), {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 1, 16}, 51] (*  Harvey P. Dale, May 07 2011 *) PROG (PARI) a(n)=n*(7*n-6) \\ Charles R Greathouse IV, Jan 24 2014 CROSSREFS Sequence in context: A192143 A221593 A300962 * A209993 A318093 A223029 Adjacent sequences:  A051865 A051866 A051867 * A051869 A051870 A051871 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Dec 15 1999 STATUS approved

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Last modified November 16 21:47 EST 2018. Contains 317275 sequences. (Running on oeis4.)