A129954 Second differences of A129952.

1, 3, 6, 14, 32, 72, 160, 352, 768, 1664, 3584, 7680, 16384, 34816, 73728, 155648, 327680, 688128, 1441792, 3014656, 6291456, 13107200, 27262976, 56623104, 117440512, 243269632, 503316480, 1040187392, 2147483648, 4429185024

Offset

0,2

Comments

First differences of A129953: a(n) = A129953(n+1) - A129953(n).

Essentially the same as A078836: a(n) = A078836(n+4) for n > 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

a(0) = 1, a(1) = 3; for n > 1, a(n) = (n+4)*2^(n-2).

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

Binomial transform of [1, 2, 1, 4, 1, 6, 1, 8, ...]. - Gary W. Adamson, Sep 29 2007

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] ]; U:=[ T[n+1]-T[n]: n in[1..2*m-1] ]; [ U[n+1]-U[n]: n in[1..2*m-2] ]; // Klaus Brockhaus, Jun 17 2007
(PARI) {m=29; print1(1, ", ", 3, ", "); for(n=2, m, print1((n+4)*2^(n-2), ", "))} \\ Klaus Brockhaus, Jun 17 2007

Crossrefs

Cf. A129952, A129953, A078836.

Sequence in context: A077998 A209357 A090165 * A238768 A272362 A182905

Adjacent sequences: A129951 A129952 A129953 * A129955 A129956 A129957

Keyword

nonn,easy

Author

Paul Curtz, Jun 10 2007

Extensions

Edited and extended by Klaus Brockhaus, Jun 17 2007

Status

approved