A129955 Third differences of A129952.

2, 3, 8, 18, 40, 88, 192, 416, 896, 1920, 4096, 8704, 18432, 38912, 81920, 172032, 360448, 753664, 1572864, 3276800, 6815744, 14155776, 29360128, 60817408, 125829120, 260046848, 536870912, 1107296256, 2281701376, 4697620480

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4, -4).

Formula

First differences of A129954: a(n) = A129954(n+1) - A129954(n).

a(n) = A034007(n+2)-2^(n-2) for n > 1.

a(0) = 2, a(1) = 3; for n > 1, a(n) = (n+6)*2^(n-2).

G.f.: (2-5*x+4*x^2-2*x^3)/(1-2*x)^2.

From Amiram Eldar, Jan 13 2021: (Start)

Sum_{n>=0} 1/a(n) = 256*log(2) - 12347/70.

Sum_{n>=0} (-1)^n/a(n) = 21851/210 - 256*log(3/2). (End)

Mathematica

Differences[LinearRecurrence[{4, -4}, {1, 1, 2, 6}, 40], 3] (* Harvey P. Dale, Sep 04 2020 *)

Prog

(Magma) m:=17; S:=&cat[ [ 1, 2*i ]: i in [0..m] ]; T:=[ &+[ Binomial(j-1, k-1)*S[k]: k in [1..j] ]: j in [1..2*m] ]; U:=[ T[n+1]-T[n]: n in[1..2*m-1] ]; V:=[ U[n+1]-U[n]: n in[1..2*m-2] ]; [ V[n+1]-V[n]: n in[1..2*m-3] ]; // Klaus Brockhaus, Jun 17 2007
(PARI) {m=29; print1(2, ", ", 3, ", "); for(n=2, m, print1((n+6)*2^(n-2), ", "))} \\ Klaus Brockhaus, Jun 17 2007

Crossrefs

Cf. A129952, A129953, A129954, A034007.

Sequence in context: A368882 A036746 A232165 * A034066 A034076 A272642

Adjacent sequences: A129952 A129953 A129954 * A129956 A129957 A129958

Keyword

nonn

Author

Paul Curtz, Jun 10 2007

Extensions

Edited and extended by Klaus Brockhaus, Jun 17 2007

Status

approved