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A "Morgan Voyce" transform of A103210.
2

%I #15 May 24 2016 10:24:58

%S 1,4,25,187,1552,13771,127927,1228576,12099751,121538581,1240336660,

%T 12824049277,134043231781,1414108869268,15037450664317,

%U 161014687970191,1734550886346592,18785969304551263,204432608804093155

%N A "Morgan Voyce" transform of A103210.

%C Partial sums of A166696.

%H G. C. Greubel, <a href="/A166697/b166697.txt">Table of n, a(n) for n = 0..500</a>

%F G.f.: (1-3x+x^2-sqrt(1-14x+27x^2-14x^3+x^4))/(4x(1-x));

%F G.f.: 1/(1-x-3x/(1-x-2x/(1-x-3x/(1-x-2x/(1-x-3x/(1-x-2x/(1-.... (continued fraction);

%F a(n) = Sum_{k=0..n} C(n+k,2k)*A103210(k).

%F a(n) = Sum_{k=0..n} A085478(n,k)*A103210(k). - _Philippe Deléham_, Nov 16 2013

%F Conjecture: (n+1)*a(n) + 3*(-5*n+2)*a(n-1) + (41*n-61)*a(n-2) + (-41*n+103)*a(n-3) + 3*(5*n-18)*a(n-4) + (-n+5)*a(n-5) = 0. - _R. J. Mathar_, Feb 10 2015

%p A166697 := proc(n)

%p add(A166696(k),k=0..n) ;

%p end proc: # _R. J. Mathar_, Feb 10 2015

%t CoefficientList[Series[(1 - 3*t + t^2 - Sqrt[1 - 14*t + 27*t^2 - 14*t^3 + t^4])/(4*t*(1 - t)), {t, 0, 50}], t] (* _G. C. Greubel_, May 23 2016 *)

%Y Cf. A085478, A103210, A166696

%K easy,nonn

%O 0,2

%A _Paul Barry_, Oct 18 2009