This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A153772 a(n) = (2^n + 2*(-1)^n - 6)/3. 3
 -1, -2, 0, 0, 4, 8, 20, 40, 84, 168, 340, 680, 1364, 2728, 5460, 10920, 21844, 43688, 87380, 174760, 349524, 699048, 1398100, 2796200, 5592404, 11184808, 22369620, 44739240, 89478484, 178956968, 357913940, 715827880 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The array of T(n,k) with T(0,k) = A141325(k) and successive differences T(n,k) = T(n-1,k+1) - T(n-1,k) in further rows is 1, 1, 1, 1, 3, 5, 9, 13, 21, 33, 55,.. 0, 0, 0, 2, 2, 4, 4, 8, 12, 22,.. 0, 0, 2, 0, 2, 0, 4, 4, 10,... 0, 2, -2, 2, -2, 4, 0, 6,.. 2, -4, 4, -4, 6, -4, 6,.. -6, 8, -8, 10, -10, 10,... with T(n,n) = A078008(n), T(n,n+1) = -A167030(n), T(n,n+2) = A128209(n), T(n,n+3) = -a(n). All these sequences along the diagonals obey the recurrences a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) and a(n) = 5*a(n-2) - 4*a(n-4). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (2,1,-2). FORMULA a(n) = A078008(n) - 2. a(n) = +2*a(n-1) +a(n-2) -2*a(n-3). a(n) = a(n-1) + 2*a(n-2) + 4. G.f.: (1 - 5*x^2) / ( (1-x)*(2*x-1)*(1+x) ). E.g.f.: (1/3)*(2*exp(-x) - 6*exp(x) + exp(2*x)). - G. C. Greubel, Aug 27 2016 MATHEMATICA Table[(2^n + 2*(-1)^n - 6)/3, {n, 0, 25}] (* or *) LinearRecurrence[{2, 1, -2}, {-1, -2, 0}, 25] (* G. C. Greubel, Aug 27 2016 *) PROG (MAGMA) [2^n/3 +2*(-1)^n/3-2: n in [0..40]]; // Vincenzo Librandi, Aug 07 2011 (PARI) a(n)=(2^n+2*(-1)^n-6)/3 \\ Charles R Greathouse IV, Aug 28 2016 CROSSREFS Sequence in context: A021837 A236934 A155719 * A197007 A011449 A231037 Adjacent sequences:  A153769 A153770 A153771 * A153773 A153774 A153775 KEYWORD easy,sign AUTHOR Paul Curtz, Jan 01 2009 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 24 14:13 EDT 2019. Contains 326283 sequences. (Running on oeis4.)