The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A331319 a(n) = [x^n](x - 2*x^3)/(1 - 2*x*(x + 1))^2. 3
 0, 1, 4, 14, 48, 156, 496, 1544, 4736, 14352, 43072, 128224, 379136, 1114560, 3260160, 9494656, 27545600, 79642880, 229573632, 659951104, 1892478976, 5414755328, 15461117952, 44064835584, 125371383808, 356137570304, 1010187124736, 2861518086144, 8095486246912 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (4,0,-8,-4). FORMULA a(n) = Sum_{k=0..n} A322942(n, k)*k. a(n) = 2*((n^2 - n - 2)*a(n-2) + (n^2 - 2*n - 4)*a(n-1))/(n^2 - 3*n). a(n) = n! [x^n] (1/9)*exp(x)*(sqrt(3)*(3*x+2)*sinh(sqrt(3)*x)+3*x*cosh(sqrt(3)*x)). From Colin Barker, Jan 14 2020: (Start) a(n) = ((1-sqrt(3))^n*(-2*sqrt(3) + 3*n) + (1+sqrt(3))^n*(2*sqrt(3) + 3*n)) / 18. a(n) = 4*a(n-1) - 8*a(n-3) - 4*a(n-4) for n>3. (End) MAPLE gf := (x - 2*x^3)/(1 - 2*x*(x + 1))^2: ser := series(gf, x, 32): seq(coeff(ser, x, n), n=0..28); MATHEMATICA LinearRecurrence[ {4, 0, -8, -4}, {0, 1, 4, 14}, 28] PROG (PARI) concat(0, Vec(x*(1 - 2*x^2) / (1 - 2*x - 2*x^2)^2 + O(x^30))) \\ Colin Barker, Jan 14 2020 CROSSREFS Cf. A322942 (Jacobsthal triangle), A331320, A331321. Sequence in context: A022632 A027906 A047135 * A291254 A307127 A248957 Adjacent sequences: A331316 A331317 A331318 * A331320 A331321 A331322 KEYWORD nonn,easy AUTHOR Peter Luschny, Jan 14 2020 STATUS approved

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

Last modified February 25 06:40 EST 2024. Contains 370310 sequences. (Running on oeis4.)