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A129954 Second differences of A129952. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 11 01:30 EDT 2020. Contains 335600 sequences. (Running on oeis4.)