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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
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
A. S. Fraenkel and C. Kimberling, Generalized Wythoff arrays, shuffles and interspersions, Discr. Math. 126 (1-3) (1994) 137-149.
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). [R. J. Mathar, Aug 17 2009]
a(n) = a(n-1) + a(n-2) * A000034(n-1). [Reinhard Zumkeller, Jan 21 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
Sequence in context: A025084 A134512 A106523 * A121720 A056515 A056516
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 June 19 05:57 EDT 2024. Contains 373492 sequences. (Running on oeis4.)