A153797 7 times octagonal numbers: a(n) = 7*n*(3*n-2).
0, 7, 56, 147, 280, 455, 672, 931, 1232, 1575, 1960, 2387, 2856, 3367, 3920, 4515, 5152, 5831, 6552, 7315, 8120, 8967, 9856, 10787, 11760, 12775, 13832, 14931, 16072, 17255, 18480, 19747, 21056, 22407, 23800, 25235, 26712, 28231
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Magma
[ 7*n*(3*n-2): n in [0..40] ];
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Mathematica
s=0;lst={s};Do[s+=n;AppendTo[lst,s],{n,7,8!,42}];lst (* Vladimir Joseph Stephan Orlovsky, Apr 03 2009 *) Table[7*n*(3*n-2), {n,0,25}] (* or *) LinearRecurrence[{3,-3,1},{0,7,56},25] (* G. C. Greubel, Aug 29 2016 *) 7*PolygonalNumber[8,Range[0,40]] (* Harvey P. Dale, May 16 2025 *) -
PARI
a(n)=7*n*(3*n-2) \\ Charles R Greathouse IV, Aug 29 2016
Formula
a(n) = 21*n^2 - 14*n = 7*A000567(n).
a(n) = a(n-1) + 42*n - 35 (with a(0)=0). - Vincenzo Librandi, Nov 27 2010
From G. C. Greubel, Aug 29 2016: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: 7*x*(1 + 5*x)/(1 - x)^3.
E.g.f.: 7*x*(1 + 3*x)*exp(x). (End)