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

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A174814 a(n) = n*(n+1)*(5*n+1)/3. 2

%I #36 Sep 08 2022 08:45:51

%S 0,4,22,64,140,260,434,672,984,1380,1870,2464,3172,4004,4970,6080,

%T 7344,8772,10374,12160,14140,16324,18722,21344,24200,27300,30654,

%U 34272,38164,42340,46810,51584,56672,62084,67830,73920,80364,87172,94354,101920,109880

%N a(n) = n*(n+1)*(5*n+1)/3.

%C Also zero followed by bisection (even part) of A088003.

%C Numbers ending in 0, 2 or 4 (cf. 2*A053796(n)). Therefore we can easily see that a(m)^(2*k+1)==-1 (mod 5) only for m in A047219, while a(m)^(2*k)==-1 (mod 5) only for m in A016873 and k odd.

%H Vincenzo Librandi, <a href="/A174814/b174814.txt">Table of n, a(n) for n = 0..2000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F G.f.: 2*x*(2+3*x)/(1-x)^4.

%F a(n) = 2*A033994(n) for n>0.

%F a(n) = n*A147875(n+1)-sum(k=1..n, A147875(k)) for n>0.

%F a(-n) = -A144945(n).

%t Table[1/3 n (1+n) (1+5 n), {n,0,50}] (* _Harvey P. Dale_, Feb 25 2011 *)

%o (Magma) [n*(n+1)*(5*n+1)/3: n in [0..50]]; // _Vincenzo Librandi_, May 30 2011

%o (PARI) a(n) = n*(n+1)*(5*n+1)/3 \\ _Charles R Greathouse IV_, May 30 2011

%K nonn,easy

%O 0,2

%A _Bruno Berselli_, Dec 01 2010 - Dec 02 2010

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)