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

Offset: 0

Author

Paul Curtz, Jun 10 2007

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-4).

Crossrefs

Cf. A129952, A087447.

Programs

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<1 else n # Chai Wah Wu, Oct 03 2024

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.

Extensions

Edited and extended by Klaus Brockhaus, Jun 17 2007