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

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)];

Crossrefs

Sequence in context: A175148 A147417 A147357 * A213046 A262021 A221181

Adjacent sequences: A004135 A004136 A004137 * A004139 A004140 A004141

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Entry revised by N. J. A. Sloane, Jun 29 2017

Status

approved