A026244 a(n) = 4^n*(4^n+1)/2.

1, 10, 136, 2080, 32896, 524800, 8390656, 134225920, 2147516416, 34359869440, 549756338176, 8796095119360, 140737496743936, 2251799847239680, 36028797153181696, 576460752840294400, 9223372039002259456, 147573952598266347520, 2361183241469182345216

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

Cf. A052539.

Sequence in context: A128862 A129803 A065024 * A371405 A261503 A096619

Adjacent sequences: A026241 A026242 A026243 * A026245 A026246 A026247

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved