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A sequence satisfying (a(2n+1) + 1)^3 = Sum_{k=1..2n+1} a(k)^3.
(Formerly M4073 N1688)
2

%I M4073 N1688 #28 Apr 01 2017 04:03:30

%S 1,6,8,262,2448,17997702,44082372248,5829766629386380698502,

%T 256989942683351711945337288361248,

%U 198131491921177194311506308094238133848780474484255622782351242502

%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 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)=1, a(2)=6, a(3)=8, 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] = 1; a[2] = 6; a[3] = 8; 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]; Array[a, 10] (* _Jean-François Alcover_, Feb 15 2016, after _Sean A. Irvine_ *)

%K nonn

%O 1,2

%A _N. J. A. Sloane_

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