A002082 2nd differences are periodic. (Formerly M0335 N0127)

2, 2, 4, 10, 16, 28, 48, 76, 110, 144, 182, 222, 264, 310, 356, 408, 468, 536, 610, 684, 762, 842, 924, 1010, 1096, 1188, 1288, 1396, 1510, 1624, 1742, 1862, 1984, 2110, 2236, 2368

Offset

0,1

References

"On the Determination of the General Term of a New Class of Infinite Series", by Charles Babbage, Trans. Camb. Phil. Soc., 2 (1827), 217-225 (see p. 220).

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=0..35.

Index entries for linear recurrences with constant coefficients, signature (3, -4, 4, -4, 4, -4, 4, -4, 4, -3, 1).

Formula

G.f.: (-4x^10+2x^9-2x^8-4x^7-4x^6-4x^5-2x^4+2x^3-6x^2+4x-2)/((x^4-x^3+x^2-x+1)*(x^4+x^3+x^2+x+1)*(x-1)^3). - Ralf Stephan, Mar 11 2003

Mathematica

LinearRecurrence[{3, -4, 4, -4, 4, -4, 4, -4, 4, -3, 1}, {2, 2, 4, 10, 16, 28, 48, 76, 110, 144, 182}, 36] (* Ray Chandler, Aug 25 2015 *)

Crossrefs

Cf. A002081.

Sequence in context: A102623 A216695 A320069 * A005304 A152732 A308986

Adjacent sequences: A002079 A002080 A002081 * A002083 A002084 A002085

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved