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A027983 T(n,n+1) + T(n,n+2) + ... + T(n,2n), T given by A027960. 1

%I

%S 1,5,14,35,81,180,389,825,1726,3575,7349,15020,30561,61965,125294,

%T 252795,509161,1024100,2057549,4130225,8284926,16609455,33282989,

%U 66669660,133507081,267285605,535010414,1070731475,2142612801

%N T(n,n+1) + T(n,n+2) + ... + T(n,2n), T given by A027960.

%C Is this the same as A027974? - _R. J. Mathar_, Oct 23 2008

%H Philipp Emanuel Weidmann, <a href="http://worldwidemann.com/the-sequencer-oeis-survey/">The Sequencer OEIS Survey</a>

%H Susanne Wienand, <a href="https://oeis.org/w/images/b/bc/Suggestion_for_a_proof_%28conjecture_of_sequencer%29.pdf">Suggestion for a proof of Philipp Emanuel Weidman's conjecture concerning A027983</a>

%F Conjectured formula: a(n) = 2 * a(n - 1) + L(n + 1), where L(m) is the m-th Lucas number, as in A000032. - _David A. Corneth_, Apr 16 2015

%F Conjectures from _Colin Barker_, Feb 17 2016: (Start)

%F a(n) = 2^(-1-n)*(4^(2+n)+(1-sqrt(5))^n*(-7+3*sqrt(5))-(1+sqrt(5))^n*(7+3*sqrt(5))).

%F a(n) = 3*a(n-1)-a(n-2)-2*a(n-3) for n>2.

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

%F (End)

%K nonn

%O 0,2

%A _Clark Kimberling_

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Last modified November 14 22:17 EST 2019. Contains 329134 sequences. (Running on oeis4.)