OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
P. J. Szablowski, On moments of Cantor and related distributions, arXiv preprint arXiv:1403.0386 [math.PR], 2014.
Index entries for linear recurrences with constant coefficients, signature (20,-64)
FORMULA
From Paul Barry, Mar 11 2004: (Start)
With interpolated zeros 0, 1, 0, 10, ... has a(n) = (4^n - (-4)^n + 2*2^n - 2*(-2)^n)/16 and counts walks of length n between adjacent vertices of the 4-cube.
G.f.: (1 - 10*x)/((1 - 4*x)*(1 - 16*x)). (End)
From Philippe Deléham, Sep 08 2009: (Start)
a(n) = Sum_{k = 0..n} 9*k*binomial(2n, 2k) = Sum_{k = 0..n} 9^k*A086645(n, k);
a(n) = 8^n*T(n,5/4) where T is the Chebyshev polynomial of first kind;
e.g.f.: exp(10*x)*cosh(6*x). (End)
a(n) = (2*(n+1))! * [x^(2*(n+1))] (cosh(x)^4-1)/4. - Vladimir Kruchinin, Oct 19 2016
a(n) = 64^n * a(-n) for all n in Z. - Michael Somos, Jul 02 2017
MAPLE
seq(binomial(-4^n, 2), n=0..18); # Zerinvary Lajos, Feb 22 2008
MATHEMATICA
Table[4^n (4^n + 1)/2, {n, 0, 19}] (* Alonso del Arte, Jun 18 2019 *)
PROG
(Magma) [4^n*(4^n+1)/2: n in [0..30]]; // Vincenzo Librandi, May 01 2011
(PARI) a(n)=4^n*(4^n+1)/2 \\ Charles R Greathouse IV, Oct 07 2015
(Scala) ((List.fill(20)(4: BigInt)).scanLeft(1: BigInt)(_ * _)).map((n: BigInt) => n * (n + 1)/2) // Alonso del Arte, Jun 22 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved