A002082 2nd differences are periodic.

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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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

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

Crossrefs

Cf. A002081.

Programs

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 *)

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