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 A051869 17-gonal (or heptadecagonal) numbers: n*(15*n-13)/2. 13

%I

%S 0,1,17,48,94,155,231,322,428,549,685,836,1002,1183,1379,1590,1816,

%T 2057,2313,2584,2870,3171,3487,3818,4164,4525,4901,5292,5698,6119,

%U 6555,7006,7472,7953,8449,8960,9486,10027,10583,11154,11740,12341

%N 17-gonal (or heptadecagonal) numbers: n*(15*n-13)/2.

%C Sequence found by reading the line from 0, in the direction 0, 17,... and the parallel line from 1, in the direction 1, 48,..., in the square spiral whose vertices are the generalized 17-gonal numbers. - _Omar E. Pol_, Jul 18 2012

%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="/A051869/b051869.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 G.f.: x*(1+14*x)/(1-x)^3. - _Bruno Berselli_, Feb 04 2011

%F a(n) = a(n-1) + 15*n - 14 with n>0, a(0)=0. - _Vincenzo Librandi_, Aug 06 2010

%F a(n) = A226489(n) - n. - _Bruno Berselli_, Jun 11 2013

%F a(15*a(n) + 106*n + 1) = a(15*a(n) + 106*n) + a(15*n+1). - _Vladimir Shevelev_, Jan 24 2014

%F E.g.f.: x*(2 + 15*x)*exp(x)/2. - _G. C. Greubel_, Aug 30 2019

%p A051869 := proc(n) n*(15*n-13)/2 ; end proc: seq(A051869(n),n=0..30) ; # _R. J. Mathar_, Feb 05 2011

%t Table[n*(15*n - 13)/2, {n,0,40}] (* _Robert Price_, Oct 11 2018 *)

%o (PARI) a(n)=n*(15*n-13)/2 \\ _Charles R Greathouse IV_, Jan 24 2014

%o (MAGMA) [n*(15*n-13)/2: n in [0..40]]; // _G. C. Greubel_, Aug 30 2019

%o (Sage) [n*(15*n-13)/2 for n in (0..40)] # _G. C. Greubel_, Aug 30 2019

%o (GAP) List([0..40], n-> n*(15*n-13)/2); # _G. C. Greubel_, Aug 30 2019

%Y Cf. A002378.

%K nonn,easy

%O 0,3

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

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Last modified November 17 18:24 EST 2019. Contains 329241 sequences. (Running on oeis4.)