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

0,3

Links

Table of n, a(n) for n=0..61.

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

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

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 *)

Prog

(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)
(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

Crossrefs

Cf. A137797.

Sequence in context: A110652 A354778 A059373 * A312754 A312755 A312756

Adjacent sequences: A137795 A137796 A137797 * A137799 A137800 A137801

Keyword

easy,nonn

Author

William A. Tedeschi, Feb 10 2008

Status

approved