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 A007068 a(n) = a(n-1) + (3+(-1)^n)*a(n-2)/2. (Formerly M2360) 11
 1, 3, 4, 10, 14, 34, 48, 116, 164, 396, 560, 1352, 1912, 4616, 6528, 15760, 22288, 53808, 76096, 183712, 259808, 627232, 887040, 2141504, 3028544, 7311552, 10340096, 24963200, 35303296, 85229696, 120532992, 290992384, 411525376 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS First row of spectral array W(sqrt 2). Row sums of the square of the matrix with general term binomial(floor(n/2),n-k). - Paul Barry, Feb 14 2005 REFERENCES A. Fraenkel and C. Kimberling, "Generalized Wythoff arrays, shuffles and interspersions," Discrete Mathematics 126 (1994) 137-149. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (0,4,0,-2). FORMULA a(2n+1)=a(2n)+a(2n-1); a(2n)=a(2n-1)+2*a(2n-2); same recurrence (mod parity) as A001882) - Len Smiley, Feb 05 2001. a(n)=sum{k=0..n, sum{j=0..n, C(floor(n/2), n-j)*C(floor(j/2), j-k)}} - Paul Barry, Feb 14 2005 a(n)=4*a(n-2)-2*a(n-4). G.f.: -x*(1+x)*(2*x^2-2*x-1)/(1-4*x^2+2*x^4). a(2n+1)=A007070(n). a(2n)=A007052(n). [From R. J. Mathar, Aug 17 2009] a(n) = a(n-1) + a(n-2) * A000034(n-1). [Reinhard Zumkeller, Jan 21 2012] a(n)=(1-1/2*(-1)^n)*((2-sqrt(2))^(1/4*(2*n+(-1)^n-1))+(2+sqrt(2))^(1/4*(2*n+(-1)^n-1)))+(1/4*sqrt(2)*(-1)^n-3/4*sqrt(2))*((2-sqrt(2))^(1/4*(2*n+(-1)^n-1))-(2+sqrt(2))^(1/4*(2*n+(-1)^n-1))). - Paolo P. Lava, Feb 13 2012 MATHEMATICA RecurrenceTable[{a[1]==1, a[2]==3, a[n]==a[n-1]+(3+(-1)^n) a[n-2]/2}, a[n], {n, 40}] (* Harvey P. Dale, Nov 12 2012 *) PROG (Haskell) a007068 n = a007068_list !! (n-1) a007068_list = 1 : 3 : zipWith (+)    (tail a007068_list) (zipWith (*) a000034_list a007068_list) -- Reinhard Zumkeller, Jan 21 2012 CROSSREFS Cf. A062112. Sequence in context: A025084 A134512 A106523 * A121720 A056515 A056516 Adjacent sequences:  A007065 A007066 A007067 * A007069 A007070 A007071 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS Better description and more terms from Olivier Gérard, Jun 05 2001 STATUS approved

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Last modified August 3 11:42 EDT 2020. Contains 336198 sequences. (Running on oeis4.)