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!)
A196514 Partial sums of A100381. 1
0, 4, 28, 124, 444, 1404, 4092, 11260, 29692, 75772, 188412, 458748, 1097724, 2588668, 6029308, 13893628, 31719420, 71827452, 161480700, 360710140, 801112060, 1769996284, 3892314108, 8522825724, 18589155324, 40399536124, 87509958652 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Like any sequence with a linear recurrence, this has a Pisano period length modulo any k >= 1. The period lengths for this sequence are (modulo k >= 1) 1, 1, 6, 1, 20, 6, 21, 1, 18, 20, 110, 6, 156, 21, 60, 1, 136, 18, 342, 20, ....
REFERENCES
Jolley, Summation of Series, Dover (1961), eq (53) page 10.
LINKS
FORMULA
G.f.: 4*x / ( (x-1)*(2*x-1)^3 ).
a(n) = (n^2 - n + 2)*2^(n+1) - 4 = 4*A055580(n-1).
a(n) = 7*a(n-1) - 18*a(n-2) + 20*a(n-3) - 8*a(n-4); a(0)=0, a(1)=4, a(2)=28, a(3)=124. - Harvey P. Dale, Jan 12 2016
MATHEMATICA
Table[2^n*Binomial[n, 2], {n, 1, 27}] // Accumulate (* Jean-François Alcover, Jun 24 2013 *)
LinearRecurrence[{7, -18, 20, -8}, {0, 4, 28, 124}, 30] (* Harvey P. Dale, Jan 12 2016 *)
PROG
(Magma) [(n^2-n+2)*2^(n+1)-4 : n in [0..30]]; // Vincenzo Librandi, Oct 05 2011
(PARI) a(n)=(n^2-n+2)<<(n+1)-4 \\ Charles R Greathouse IV, Oct 05 2011
CROSSREFS
Sequence in context: A318011 A328685 A212900 * A249629 A131459 A231581
KEYWORD
nonn,easy,less,changed
AUTHOR
R. J. Mathar, Oct 03 2011
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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 18 03:33 EDT 2024. Contains 371767 sequences. (Running on oeis4.)