A137798 Partial sums of A137797.

0, 0, 4, 8, 16, 14, 16, 18, 24, 30, 30, 30, 34, 38, 46, 44, 46, 48, 54, 60, 60, 60, 64, 68, 76, 74, 76, 78, 84, 90, 90, 90, 94, 98, 106, 104, 106, 108, 114, 120, 120, 120, 124, 128, 136, 134, 136, 138, 144, 150, 150, 150, 154, 158, 166, 164, 166, 168, 174, 180, 180, 180

Offset: 0

Author

William A. Tedeschi, Feb 10 2008

Keywords

• easy
• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (0,1,0,0,1,0,-1).

Crossrefs

Cf. A137797.

Programs

Mathematica

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 *)

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

Python

sequence = []
l = list(range(20))
while len(l) > 0:
    a = l.pop(0)
    z = sum(2*((x+1)%5)-2*((x+1)%2) for x in range(a))
    sequence.append(z)
print(sequence)

Formula

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

a(n) = a(n-2)+a(n-5)-a(n-7) for n>6. - Colin Barker, Dec 16 2014

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