%I #25 Sep 08 2022 08:45:24

%S 11,61,281,911,2311,4961,9461,16531,27011,41861,62161,89111,124031,

%T 168361,223661,291611,374011,472781,589961,727711,888311,1074161,

%U 1287781,1531811,1809011,2122261,2474561,2869031,3308911,3797561,4338461,4935211,5591531

%N a(n) = 5*n^4 - 10*n^3 + 20*n^2 - 15*n + 11.

%H Vincenzo Librandi, <a href="/A115565/b115565.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5, -10, 10, -5, 1).

%F a(1-n) = a(n) = 5*(n^2-n)^2 +15*(n^2-n) +11. - _Michael Somos_, May 15 2006

%F a(1)=11, a(2)=61, a(3)=281, a(4)=911, a(5)=2311, a(n)=5*a(n-1)-10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5). - _Harvey P. Dale_, Oct 03 2011

%F G.f.: x*(11+6*x+86*x^2+6*x^3+11*x^4)/(1-x)^5. - _Wesley Ivan Hurt_, Aug 22 2015

%p A115565:=n->5*n^4 - 10*n^3 + 20*n^2 - 15*n + 11: seq(A115565(n), n=1..40); # _Wesley Ivan Hurt_, Aug 22 2015

%t Table[5n^4-10n^3+20n^2-15n+11,{n,40}] (* or *) LinearRecurrence[ {5,-10,10,-5,1},{11,61,281,911,2311},40] (* _Harvey P. Dale_, Oct 03 2011 *)

%t CoefficientList[Series[(11 + 6 x + 86 x^2 + 6 x^3 + 11 x^4)/(1 - x)^5, {x, 0, 40}], x] (* _Wesley Ivan Hurt_, Aug 22 2015 *)

%o ay1[1] := 11; a[1] :=50; b[1] :=170; c[1] :=240; k := 120; Repeat ay1[1] := ay1[1] + a[1]; a[1] := a[1] + b[1]; b[1] := b[1] + c[1]; c[1] := c[1] + k; writeln(ay1[1]); Until 1 < 0;

%o (Magma) [5*(n^2-n)^2 +15*(n^2-n) +11: n in [1..40]]; // _Vincenzo Librandi_, Oct 04 2011

%o (PARI) a(n) = 5*n^4 - 10*n^3 + 20*n^2 - 15*n + 11 \\ _Charles R Greathouse IV_, Aug 22 2015

%o (PARI) first(m)=vector(m,i,5*i^4 - 10*i^3 + 20*i^2 - 15*i + 11) \\ _Anders Hellström_, Aug 22 2015

%K nonn,easy

%O 1,1

%A Aldrich Stevens (Aldrichstevens(AT)msn.com), Mar 11 2006

%E Checked by _N. J. A. Sloane_, Mar 29 2006

%E Edited by _N. J. A. Sloane_, Jun 13 2008