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 A128209 Jacobsthal numbers(A001045) + 1. 13

%I

%S 1,2,2,4,6,12,22,44,86,172,342,684,1366,2732,5462,10924,21846,43692,

%T 87382,174764,349526,699052,1398102,2796204,5592406,11184812,22369622,

%U 44739244,89478486,178956972,357913942,715827884,1431655766,2863311532,5726623062

%N Jacobsthal numbers(A001045) + 1.

%C Row sums of A128208.

%C Essentially the same as A052953. - _R. J. Mathar_, Jun 14 2008

%C 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

%C 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

%D V. S. Shevelyov (Shevelev), Extension of the Moser class of four-line Latin rectangles, DAN Ukrainy, 3(1992),15-19. [From _Vladimir Shevelev_, Apr 12 2010]

%H Vincenzo Librandi, <a href="/A128209/b128209.txt">Table of n, a(n) for n = 0..1000</a>

%H D. H. Lehmer, <a href="/A002487/a002487_1.pdf">On Stern's Diatomic Series</a>, Amer. Math. Monthly 36(1) 1929, pp. 59-67. [Annotated and corrected scanned copy]

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-2).

%F a(n) = 1 + 2^n/3 - (-1)^n/3.

%F G.f.: (1-3*x^2)/(1 - 2*x - x^2 + 2*x^3).

%t CoefficientList[Series[(1-3*x^2)/(1-2*x-x^2+2*x^3),{x,0,40}],x] (* _Vladimir Joseph Stephan Orlovsky_, Jan 31 2012 *)

%o (MAGMA) [1+2^n/3-(-1)^n/3: n in [0..40]]; // _Vincenzo Librandi_, Aug 11 2011

%o (PARI) a(n)=2^n\/3+1 \\ _Charles R Greathouse IV_, Jan 31 2012

%Y Cf. A167030, A153643, A049456.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Feb 19 2007

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Last modified April 11 08:10 EDT 2021. Contains 342886 sequences. (Running on oeis4.)