|
| |
|
|
A130755
|
|
Binomial transform of periodic sequence (3, 1, 2).
|
|
7
| |
|
|
3, 4, 7, 15, 32, 65, 129, 256, 511, 1023, 2048, 4097, 8193, 16384, 32767, 65535, 131072, 262145, 524289, 1048576, 2097151, 4194303, 8388608, 16777217, 33554433, 67108864, 134217727, 268435455, 536870912, 1073741825, 2147483649
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,1
|
|
|
COMMENTS
| The third sequence of "less twisted numbers"; this sequence, A130750 and A130752 form a "suite en trio" (cf. reference, p. 130).
First differences of A130752, second differences of A130750.
Sequence equals its third differences:
3.....4.....7....15....32....65...129...256...511..1023...
....1.....3.....8....17....33....64...127...255...512...
.......2.....5.....9....16....31....63...128...257...
..........3.....4.....7....15....32....65...129...
|
|
|
REFERENCES
| P. Curtz, Exercise Book, manuscript, 1995.
|
|
|
LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..300
Index entries for sequences related to linear recurrences with constant coefficients, signature (3,-3,2).
|
|
|
FORMULA
| G.f.: (3-5*x+4*x^2)/((1-2*x)*(1-x+x^2)).
a(0) = 3; a(1) = 4; a(2) = 7; for n > 2, a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3).
a(n) = 2^(n+1) + A128834(n+2).
a(0) = 3; for n > 0, a(n) = 2*a(n-1) + A057079(n+3).
|
|
|
PROG
| (MAGMA) m:=31; S:=[ [3, 1, 2][(n-1) mod 3 +1]: n in [1..m] ]; [ &+[ Binomial(i-1, k-1)*S[k]: k in [1..i] ]: i in [1..m] ]; /* Klaus Brockhaus, Aug 03 2007 */
(PARI) {m=31; v=vector(m); v[1]=3; v[2]=4; v[3]=7; for(n=4, m, v[n]=3*v[n-1]-3*v[n-2]+2*v[n-3]); v} /* Klaus Brockhaus, Aug 03 2007 */
(PARI) {for(n=0, 30, print1(2^(n+1)+[1, 0, -1, -1, 0, 1][n%6+1], ", "))} /* Klaus Brockhaus, Aug 03 2007 */
|
|
|
CROSSREFS
| Cf. A010882 (periodic (1, 2, 3)), A128834 (periodic (0, 1, 1, 0, -1, -1)), A057079 (periodic (1, 2, 1, -1, -2, -1)), A130750 (first differences), A130752 (second differences).
Sequence in context: A024368 A187493 A027020 * A116090 A100455 A078825
Adjacent sequences: A130752 A130753 A130754 * A130756 A130757 A130758
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), Jul 13 2007
|
|
|
EXTENSIONS
| Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 03 2007
|
| |
|
|
