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A130752
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Binomial transform of periodic sequence (2, 3, 1).
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7
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2, 5, 9, 16, 31, 63, 128, 257, 513, 1024, 2047, 4095, 8192, 16385, 32769, 65536, 131071, 262143, 524288, 1048577, 2097153, 4194304, 8388607, 16777215, 33554432, 67108865, 134217729, 268435456, 536870911, 1073741823, 2147483648
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| The second sequence of "less twisted numbers"; this sequence, A130750 and A130755 form a "suite en trio" (cf. reference, p. 130).
First differences of A130750, second differences of A130755.
Sequence equals its third differences:
2.....5.....9....16....31....63...128...257...513..1024...
...3.....4.....7....15....32....65...129...256...511...
......1.....3.....8....17....33....64...127...255...
..........2.....5.....9....16....31....63...128...
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REFERENCES
| P. Curtz, Exercise Book, manuscript, 1995.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (3,-3,2).
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FORMULA
| G.f.: (2-x)/((1-2*x)*(1-x+x^2)).
a(0) = 2; a(1) = 5; a(2) = 9; for n > 2, a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3).
a(n) = 2^(n+1) + A128834(n).
a(0) = 2; for n > 0, a(n) = 2*a(n-1) + A057079(n+1).
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PROG
| (MAGMA) m:=31; S:=[ [2, 3, 1][(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]=2; v[2]=5; v[3]=9; 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)+[0, 1, 1, 0, -1, -1][n%6+1], ", "))} /* Klaus Brockhaus, Aug 03 2007 */
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CROSSREFS
| Cf. A010882 (periodic (1, 2, 3)), A128834 (periodic (0, 1, 1, 0, -1, -1)), A057079 (periodic (1, 2, 1, -1, -2, -1)), A130755 (first differences), A130750 (second differences).
Sequence in context: A056870 A014739 A039946 * A059529 A119676 A036711
Adjacent sequences: A130749 A130750 A130751 * A130753 A130754 A130755
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KEYWORD
| nonn,easy
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), Jul 13 2007
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EXTENSIONS
| Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 03 2007
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