A137798 - OEIS

%I #12 Feb 26 2024 19:16:33

%S 0,0,4,8,16,14,16,18,24,30,30,30,34,38,46,44,46,48,54,60,60,60,64,68,

%T 76,74,76,78,84,90,90,90,94,98,106,104,106,108,114,120,120,120,124,

%U 128,136,134,136,138,144,150,150,150,154,158,166,164,166,168,174,180,180,180

%N Partial sums of A137797.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,0,1,0,-1).

%F f(n) = Sum{k=0,n} 2*((k+1) mod 5) - 2*((k+1) mod 2).

%F a(n) = a(n-2)+a(n-5)-a(n-7) for n>6. - _Colin Barker_, Dec 16 2014

%F G.f.: 2*x^2*(3*x^3+6*x^2+4*x+2) / ((x-1)^2*(x+1)*(x^4+x^3+x^2+x+1)). - _Colin Barker_, Dec 16 2014

%t Accumulate[LinearRecurrence[{-1,0,0,0,1,1},{0,0,4,4,8,-2,2},100]] (* or *) LinearRecurrence[{0,1,0,0,1,0,-1},{0,0,4,8,16,14,16},100] (* _Harvey P. Dale_, Jun 08 2015 *)

%o (Python)

%o sequence = []

%o l = list(range(20))

%o while len(l) > 0:

%o     a = l.pop(0)

%o     z = sum(2*((x+1)%5)-2*((x+1)%2) for x in range(a))

%o     sequence.append(z)

%o print(sequence)

%o (PARI) concat([0,0], Vec(2*x^2*(3*x^3+6*x^2+4*x+2)/((x-1)^2*(x+1)*(x^4+x^3+x^2+x+1)) + O(x^100))) \\ _Colin Barker_, Dec 16 2014

%Y Cf. A137797.

%K easy,nonn

%O 0,3

%A _William A. Tedeschi_, Feb 10 2008