

A128209


Jacobsthal numbers(A001045) + 1.


12



1, 2, 2, 4, 6, 12, 22, 44, 86, 172, 342, 684, 1366, 2732, 5462, 10924, 21846, 43692, 87382, 174764, 349526, 699052, 1398102, 2796204, 5592406, 11184812, 22369622, 44739244, 89478486, 178956972, 357913942, 715827884, 1431655766, 2863311532, 5726623062
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


COMMENTS

Row sums of A128208.
Essentially the same as A052953.  R. J. Mathar, Jun 14 2008
Let I=I_n be the n X n identity matrix and P=P_n be the incidence matrix of the cycle (1,2,3,...,n). Then, for n >= 1, a(n+1) is the number of different representations of matrix P^(1)+I+P by sum of permutation matrices.  Vladimir Shevelev, Apr 12 2010
a(n) is the rank of Fibonacci(n+2) in row n of A049456 (regarded as an irregular triangle read by rows).  N. J. A. Sloane, Nov 23 2016


REFERENCES

V. S. Shevelyov (Shevelev), Extension of the Moser class of fourline Latin rectangles, DAN Ukrainy, 3(1992),1519. [From Vladimir Shevelev, Apr 12 2010]


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
D. H. Lehmer, On Stern's Diatomic Series, Amer. Math. Monthly 36(1) 1929, pp. 5967. [Annotated and corrected scanned copy]
Index entries for linear recurrences with constant coefficients, signature (2,1,2).


FORMULA

a(n) = 1 + 2^n/3  (1)^n/3.
G.f.: (13*x^2)/(1  2*x  x^2 + 2*x^3).


MATHEMATICA

CoefficientList[Series[(13*x^2)/(12*xx^2+2*x^3), {x, 0, 40}], x] (* Vladimir Joseph Stephan Orlovsky, Jan 31 2012 *)


PROG

(MAGMA) [1+2^n/3(1)^n/3: n in [0..40]]; // Vincenzo Librandi, Aug 11 2011
(PARI) a(n)=2^n\/3+1 \\ Charles R Greathouse IV, Jan 31 2012


CROSSREFS

Cf. A167030, A153643, A049456.
Sequence in context: A122536 A238014 A052953 * A274935 A188538 A282164
Adjacent sequences: A128206 A128207 A128208 * A128210 A128211 A128212


KEYWORD

easy,nonn


AUTHOR

Paul Barry, Feb 19 2007


STATUS

approved



