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

2, 17, 40, 5126, 211888, 134691268742, 28539643139633848, 2443533691612948322627563638932102, 69737579558305654640845711279133047105190578109248

Offset

1,1

References

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

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

Links

John Cerkan, Table of n, a(n) for n = 1..14

D. A. Klarner, Sequences of k-th powers with k-th power partial sums, Math. mag., 37 (1964), 165-167.

D. A. Klarner, Sequences of k-th powers with k-th power partial sums, Math. Mag., 37 (1964), 165-167. Annotated scanned copy.

Formula

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

Mathematica

a[1] = 2; a[2] = 17; a[3] = 40;
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];
a /@ Range[14] (* Jean-François Alcover, Oct 22 2019 *)

Crossrefs

Sequence in context: A069042 A121923 A212276 * A031906 A045390 A289135

Adjacent sequences: A000953 A000954 A000955 * A000957 A000958 A000959

Keyword

nonn

Author

N. J. A. Sloane

Extensions

One more term from Sean A. Irvine, Sep 15 2011

Status

approved