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 A123231 Row sums of A123230. 4
 1, 2, 1, 3, 2, 5, 3, 8, 5, 13, 8, 21, 13, 34, 21, 55, 34, 89, 55, 144, 89, 233, 144, 377, 233, 610, 377, 987, 610, 1597, 987, 2584, 1597, 4181, 2584, 6765, 4181, 10946, 6765, 17711, 10946, 28657, 17711, 46368, 28657, 75025, 46368, 121393, 75025, 196418 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS All terms are Fibonacci numbers A000045: a(2n-1) = Fibonacci(n), a(2n) = Fibonacci(n+2), a(2n-1) = a(2n+2). - Alexander Adamchuk, Oct 08 2006 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (0,1,0,1). FORMULA From Alexander Adamchuk, Oct 08 2006: (Start) a(n) = Fibonacci(A028242(n+2)). a(n) = Fibonacci(A030451(n+1)). a(n) = Fibonacci(3/4 -(-1)^(n+1)*3/4 +(n+1)/2). (End) a(n) = A053602(n+1) = A097594(n-5). - R. J. Mathar, Mar 08 2011 G.f. -x*(1+2*x+x^3) / ( -1+x^2+x^4 ). - R. J. Mathar, Mar 08 2011 a(n) = a(n-2) + a(n-4). - Muniru A Asiru, Oct 12 2018 MAPLE seq(coeff(series(-x*(1+2*x+x^3)/(x^4+x^2-1), x, n+1), x, n), n = 1 .. 50); # Muniru A Asiru, Oct 12 2018 MATHEMATICA p[0, x] = 1; p[1, x] = x + 1; p[k_, x_] := p[k, x] = x*p[k - 1, x] + (-1)^(n + 1)p[k - 2, x]; Table[Sum[CoefficientList[p[n, x], x][[m]], {m, 1, n + 1}], {n, 0, 20}] Rest[Flatten[Reverse/@Partition[Fibonacci[Range[30]], 2, 1]]] (* Harvey P. Dale, Mar 19 2013 *) PROG (PARI) vector(50, n, fibonacci(3/4 -(-1)^(n+1)*3/4 +(n+1)/2)) \\ G. C. Greubel, Oct 12 2018 (Magma) m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1 + 2*x + x^3)/(1 - x^2 - x^4))); // G. C. Greubel, Oct 12 2018 (GAP) a:=[1, 2, 1, 3];; for n in [5..50] do a[n]:=a[n-2]+a[n-4]; od; a; # Muniru A Asiru, Oct 12 2018 CROSSREFS Cf. A051792, A000045, A028242, A030451. Sequence in context: A051792 A053602 A272912 * A246995 A238782 A058736 Adjacent sequences: A123228 A123229 A123230 * A123232 A123233 A123234 KEYWORD nonn AUTHOR Roger L. Bagula, Oct 06 2006 EXTENSIONS More terms from Alexander Adamchuk, Oct 08 2006 STATUS approved

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Last modified July 25 01:41 EDT 2024. Contains 374585 sequences. (Running on oeis4.)