A101166 - OEIS

%I #23 Sep 08 2022 08:45:16

%S 0,4,26,94,251,555,1079,1911,3154,4926,7360,10604,14821,20189,26901,

%T 35165,45204,57256,71574,88426,108095,130879,157091,187059,221126,

%U 259650,303004,351576,405769,466001,532705,606329,687336,776204,873426

%N a(n) = (15*n^4 + 22*n^3 + 45*n^2 + 14*n) / 24.

%C a(n) = A001846(n) - A000332(n+4) = A101164(n+4,4) for n > 0.

%H Harvey P. Dale, <a href="/A101166/b101166.txt">Table of n, a(n) for n = 0..1000</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(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5), with a(0)=0, a(1)=4, a(2)=26, a(3)=94, a(4)=251. - _Harvey P. Dale_, Oct 12 2012

%F G.f.: (-x^4-4*x^3-6*x^2-4*x)/(x-1)^5. - _Harvey P. Dale_, Oct 12 2012

%t Table[(15n^4+22n^3+45n^2+14n)/24,{n,0,40}] (* or *) LinearRecurrence[ {5,-10,10,-5,1},{0,4,26,94,251},40] (* _Harvey P. Dale_, Oct 12 2012 *)

%o (Magma)[(15*n^4+22*n^3+45*n^2+14*n) / 24: n in [0..40]]; // _Vincenzo Librandi_, Dec 26 2010

%o (PARI) a(n)=(15*n^4+22*n^3+45*n^2+14*n)/24 \\ _Charles R Greathouse IV_, Oct 16 2015

%Y Cf. A005449, A101165.

%K nonn,easy

%O 0,2

%A _Reinhard Zumkeller_, Dec 03 2004