A129953 - OEIS

A129953

First differences of A129952.

0, 1, 4, 10, 24, 56, 128, 288, 640, 1408, 3072, 6656, 14336, 30720, 65536, 139264, 294912, 622592, 1310720, 2752512, 5767168, 12058624, 25165824, 52428800, 109051904, 226492416, 469762048, 973078528, 2013265920, 4160749568

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

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

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

FORMULA

a(n) = A129952(n+1) - A129952(n).

a(n) = A087447(n) for n > 0.

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

G.f.: x*(1-2*x^2)/(1-2*x)^2.

PROG

(Magma) m:=16; 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] ]; [ T[n+1]-T[n]: n in[1..2*m-1] ]; // Klaus Brockhaus, Jun 17 2007

(PARI) {m=29; print1(0, ", ", 1, ", "); for(n=2, m, print1((n+2)*2^(n-2), ", "))} \\ Klaus Brockhaus, Jun 17 2007

(Python)

def A129953(n): return n+2<<n-2 if n>1 else n # Chai Wah Wu, Oct 03 2024

CROSSREFS

Cf. A129952, A087447.

Sequence in context: A090855 A052252 A087447 * A079859 A298802 A118871

Adjacent sequences: A129950 A129951 A129952 * A129954 A129955 A129956

KEYWORD

nonn,easy,changed

AUTHOR

Paul Curtz, Jun 10 2007

EXTENSIONS

Edited and extended by Klaus Brockhaus, Jun 17 2007

STATUS

approved