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
Vincenzo Librandi, Table of n, a(n) for n = 0..3000
Index entries for linear recurrences with constant coefficients, signature (7,-18,20,-8).
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
KEYWORD
nonn,easy,less
AUTHOR
R. J. Mathar, Oct 03 2011
STATUS
approved