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4th column of number array A083075.
2

%I #18 Sep 08 2022 08:45:10

%S 1,63,229,547,1065,1831,2893,4299,6097,8335,11061,14323,18169,22647,

%T 27805,33691,40353,47839,56197,65475,75721,86983,99309,112747,127345,

%U 143151,160213,178579,198297,219415,241981,266043,291649,318847,347685

%N 4th column of number array A083075.

%H Vincenzo Librandi, <a href="/A083079/b083079.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F a(n) = 8*n^3 + 28*n^2 + 26*n + 1 = (n*(2n+3)^3 + 1)/(n+1).

%F G.f.: (1 + 59*x - 17*x^2 + 5*x^3)/(1-x)^4. - _Harvey P. Dale_, May 14 2011

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(0)=1, a(1)=63, a(2)=229, a(3)=547. - _Harvey P. Dale_, May 14 2011

%t Table[8 n^3 + 28 n^2 + 26 n + 1, {n, 0, 40}] (* or *) LinearRecurrence[ {4,-6,4,-1},{1,63,229,547},40] (* _Harvey P. Dale_, May 14 2011 *)

%o (Magma) [8*n^3+28*n^2+26*n+1: n in [0..30]]; // _Vincenzo Librandi_, Nov 12 2011

%Y Cf. A082109.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Apr 23 2003