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A000956 A sequence satisfying (a(2n+1) + 1)^3 = Sum_{k=1..2n+1} a(k)^3.
(Formerly M2099 N0831)
1

%I M2099 N0831

%S 2,17,40,5126,211888,134691268742,28539643139633848,

%T 2443533691612948322627563638932102,

%U 69737579558305654640845711279133047105190578109248

%N A sequence satisfying (a(2n+1) + 1)^3 = Sum_{k=1..2n+1} a(k)^3.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H John Cerkan, <a href="/A000956/b000956.txt">Table of n, a(n) for n = 1..14</a>

%H D. A. Klarner, <a href="http://www.jstor.org/stable/2689160">Sequences of k-th powers with k-th power partial sums</a>, Math. mag., 37 (1964), 165-167.

%H D. A. Klarner, <a href="/A000955/a000955.pdf">Sequences of k-th powers with k-th power partial sums</a>, Math. Mag., 37 (1964), 165-167. Annotated scanned copy.

%F a(1)=2, a(2)=17, a(3)=40, a(2n+2) = 3*a(2n+1)^2 + 8*a(2n+1) + 6, a(2n+3) = 3*a(2n+1)^3 + 12*a(2n+1)^2 + 17*a(2n+1) + 8. - _Sean A. Irvine_, Sep 16 2011

%t a[1] = 2; a[2] = 17; a[3] = 40;

%t a[n_] := a[n] = If[EvenQ[n], 3*a[n-1]^2 + 8*a[n-1] + 6, 3*a[n-2]^3 + 12*a[n-2]^2 + 17*a[n-2] + 8];

%t a /@ Range[14] (* _Jean-Fran├žois Alcover_, Oct 22 2019 *)

%K nonn

%O 1,1

%A _N. J. A. Sloane_

%E One more term from _Sean A. Irvine_, Sep 15 2011

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Last modified June 22 09:57 EDT 2021. Contains 345375 sequences. (Running on oeis4.)