A213779 - OEIS

%I #18 Dec 12 2016 18:24:21

%S 1,6,15,33,58,97,146,214,295,400,521,671,840,1043,1268,1532,1821,2154,

%T 2515,2925,3366,3861,4390,4978,5603,6292,7021,7819,8660,9575,10536,

%U 11576,12665,13838,15063,16377,17746,19209,20730,22350,24031,25816,27665,29623

%N Principal diagonal of the convolution array A213778.

%H Clark Kimberling, <a href="/A213779/b213779.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).

%F a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6).

%F G.f.: x*(1+4*x+2*x^2+x^3) / ((1-x)^4*(1+x)^2).

%F From _Colin Barker_, Jan 31 2016: (Start)

%F a(n) = (16*n^3+30*n^2+2*(3*(-1)^n+7)*n+3*((-1)^n-1))/48.

%F a(n) = (8*n^3+15*n^2+10*n)/24 for n even.

%F a(n) = (8*n^3+15*n^2+4*n-3)/24 for n odd.

%F (End)

%t (See A213778.)

%t LinearRecurrence[{2,1,-4,1,2,-1},{1,6,15,33,58,97},80] (* _Harvey P. Dale_, Dec 12 2016 *)

%o (PARI) Vec(x*(1+4*x+2*x^2+x^3)/((1-x)^4*(1+x)^2) + O(x^100)) \\ _Colin Barker_, Jan 31 2016

%Y Cf. A213778, A213500.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Jun 21 2012