A004138 - OEIS

A004138

From a counter moving problem.
(Formerly M0872)

1, 2, 3, 8, 13, 24, 37, 66, 107, 186, 303, 516, 849, 1436, 2377, 3998, 6639, 11134, 18531, 31024, 51701, 86464, 144205, 241018, 402163, 671906, 1121463, 1873244, 3127129, 5222724, 8719537, 14561622, 24312695, 40600230, 67790379, 113201160, 189016701, 315627944, 527024245, 880037810, 1469467515

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

REFERENCES

D. St. P. Barnard, 50 Observer Brain Twisters. Faber and Faber, London, 1962, p. 38.

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..41.

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992.

A. D. Rawlins and N. J. A. Sloane, Correspondence, 1976.

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,3,-2).

FORMULA

a(n) = a(n-1) + a(n-2) - a(n-3) + 2*a(n-4) + 2 for n >= 5. [Rawlins]

G.f. = -(-1+z^2-4*z^3+2*z^4)/((z-1)*(2*z^4-z^3+z^2+z-1)). [Conjectured (correctly) by Simon Plouffe in his 1992 dissertation.]

MAPLE

f:=proc(n) option remember;

if n <= 3 then n

elif n=4 then 8

else 2+f(n-1)+f(n-2)-f(n-3)+2*f(n-4); fi; end;

[seq(f(n), n=1..60)];