cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A024077 a(n) = 7^n - n^2.

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%I A024077 #19 Jul 08 2025 17:27:11
%S A024077 1,6,45,334,2385,16782,117613,823494,5764737,40353526,282475149,
%T A024077 1977326622,13841287057,96889010238,678223072653,4747561509718,
%U A024077 33232930569345,232630513986918,1628413597910125,11398895185372782
%N A024077 a(n) = 7^n - n^2.
%H A024077 Vincenzo Librandi, <a href="/A024077/b024077.txt">Table of n, a(n) for n = 0..500</a>
%H A024077 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (10,-24,22,-7).
%F A024077 G.f.: (1-4*x+9*x^2+6*x^3)/((1-7*x)*(1-x)^3). - _Vincenzo Librandi_, Oct 06 2014
%F A024077 a(n) = 10*a(n-1) -24*a(n-2) +22*a(n-3) -7*a(n-4) for n>3. - _Vincenzo Librandi_, Oct 06 2014
%t A024077 Table[7^n - n^2, {n, 0, 25}] (* or *) CoefficientList[Series[(1 - 4 x + 9 x^2 + 6 x^3)/((1 - 7 x) (1 - x)^3), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 06 2014 *)
%t A024077 LinearRecurrence[{10,-24,22,-7},{1,6,45,334},20] (* _Harvey P. Dale_, Sep 16 2023 *)
%o A024077 (Magma) [7^n-n^2: n in [0..25]]; // _Vincenzo Librandi_, Jul 03 2011
%o A024077 (PARI) a(n)=7^n-n^2 \\ _Charles R Greathouse IV_, Oct 06 2014
%Y A024077 Cf. similar sequences listed in A024025.
%K A024077 nonn,easy
%O A024077 0,2
%A A024077 _N. J. A. Sloane_