A000955 A sequence satisfying (a(2n+1) + 1)^3 = Sum_{k=1..2n+1} a(k)^3. (Formerly M4073 N1688)

1, 6, 8, 262, 2448, 17997702, 44082372248, 5829766629386380698502, 256989942683351711945337288361248, 198131491921177194311506308094238133848780474484255622782351242502

Offset

1,2

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

Table of n, a(n) for n=1..10.

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)=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]

Mathematica

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 *)

Crossrefs

Sequence in context: A169971 A295429 A267165 * A027721 A264518 A259129

Adjacent sequences: A000952 A000953 A000954 * A000956 A000957 A000958

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved