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A129955 Third differences of A129952. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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

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

LINKS

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

FORMULA

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.

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: A091765 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

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Last modified September 19 18:59 EDT 2020. Contains 337182 sequences. (Running on oeis4.)