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A051868
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16-gonal (or hexadecagonal) numbers: n*(7*n-6).
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3
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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; internal format)
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OFFSET
| 0,3
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REFERENCES
| A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 189.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| a(n)=n*(7*n-6).
G.f.: x*(1+13*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011
a(0)=0, a(1)=1, a(2)=16, a(n)=3*a(n-1)-3*a(n-2)+a(n-3) [From Harvey P. Dale, May 07 2011]
a(n)=14*n+a(n-1)-13 (with a(0)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 06 2010]
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EXAMPLE
| a(1)=14*1+0-13=1; a(2)=14*2+1-13=16; a(3)=14*3+16-13=45 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 06 2010]
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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 (zerinvarylajos(AT)yahoo.com), Feb 18 2008
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MATHEMATICA
| s=0; lst={s}; Do[s+=n++ +1; AppendTo[lst, s], {n, 0, 6!, 14}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 16 2008]
Table[n(7n-6), {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 1, 16}, 51] (* From Harvey P. Dale, May 07 2011 *)
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CROSSREFS
| Cf. n-gonal numbers: A000217, A000290, A000326, A000566, A000567, A001106, A001107, A051682, A051624, A051865-A051876.
Sequence in context: A173560 A204032 A192143 * A069128 A099003 A124709
Adjacent sequences: A051865 A051866 A051867 * A051869 A051870 A051871
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Dec 15 1999
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