A094506 Numerator of I(n) = (-1) * Integral_{x=0..4^n} (1-x^(3/2)) dx.

44, 1968, 65216, 2095872, 67103744, 2147463168, 68719394816, 2199022927872, 70368742866944, 2251799808442368, 72057594016956416, 2305843009129807872, 73786976294502662144, 2361183241433480429568, 75557863725908954710016

Offset

1,1

Comments

The denominator is always 5.

Links

Table of n, a(n) for n=1..15.

Index entries for linear recurrences with constant coefficients, signature (36,-128).

Formula

a(n) = -20 * 4^(n-1) + 64 * 2^(5*n-5) for n >= 1.

G.f.: 4*x*(11+96*x) / ( (32*x-1)*(4*x-1) ). - R. J. Mathar, Feb 04 2021

Mathematica

f[n_] := (-Integrate[1 - x^(3/2), {x, 0, 4^n}])5; Table[ f[n], {n, 15}] (* Robert G. Wilson v, Sep 02 2004 *)
Table[- 20 4^(n - 1) + 64 2^(5 n - 5), {n, 20}] (* Vincenzo Librandi, Jul 25 2015 *)
LinearRecurrence[{36, -128}, {44, 1968}, 20] (* Harvey P. Dale, Feb 10 2022 *)

Prog

(PARI) for(n=1, 15, print1(64*2^(5*n-5)-20*4^(n-1), ", "))
(Magma) [-20*4^(n-1)+64*2^(5*n-5): n in [1..20]]; // Vincenzo Librandi, Jul 25 2015

Crossrefs

Sequence in context: A188871 A009988 A041925 * A121008 A250446 A233941

Adjacent sequences: A094503 A094504 A094505 * A094507 A094508 A094509

Keyword

easy,nonn

Author

Al Hakanson (Hawkuu(AT)excite.com), Jun 05 2004

Extensions

Edited by Rick L. Shepherd, Jun 06 2004

Status

approved