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%I #34 Apr 04 2024 09:49:37
%S 0,4,28,124,444,1404,4092,11260,29692,75772,188412,458748,1097724,
%T 2588668,6029308,13893628,31719420,71827452,161480700,360710140,
%U 801112060,1769996284,3892314108,8522825724,18589155324,40399536124,87509958652
%N Partial sums of A100381.
%C 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, ....
%D Jolley, Summation of Series, Dover (1961), eq (53) page 10.
%H Vincenzo Librandi, <a href="/A196514/b196514.txt">Table of n, a(n) for n = 0..3000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (7,-18,20,-8).
%F G.f.: 4*x / ( (x-1)*(2*x-1)^3 ).
%F a(n) = (n^2 - n + 2)*2^(n+1) - 4 = 4*A055580(n-1).
%F 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
%t Table[2^n*Binomial[n, 2], {n, 1, 27}] // Accumulate (* _Jean-François Alcover_, Jun 24 2013 *)
%t LinearRecurrence[{7,-18,20,-8},{0,4,28,124},30] (* _Harvey P. Dale_, Jan 12 2016 *)
%o (Magma) [(n^2-n+2)*2^(n+1)-4 : n in [0..30]]; // _Vincenzo Librandi_, Oct 05 2011
%o (PARI) a(n)=(n^2-n+2)<<(n+1)-4 \\ _Charles R Greathouse IV_, Oct 05 2011
%K nonn,easy,less
%O 0,2
%A _R. J. Mathar_, Oct 03 2011
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