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A130625
First differences of A130624.
3
1, 4, 7, 11, 20, 41, 85, 172, 343, 683, 1364, 2729, 5461, 10924, 21847, 43691, 87380, 174761, 349525, 699052, 1398103, 2796203, 5592404, 11184809, 22369621, 44739244, 89478487, 178956971, 357913940, 715827881, 1431655765, 2863311532
OFFSET
0,2
COMMENTS
a(n) = A130624(n+1) - A130624(n).
FORMULA
G.f.: (1-x)*(1+2*x)/((1-2*x)*(1-x+x^2)).
a(n) = 3a(n-1) - 3a(n-2) + 2a(n-3). Sequence is identical to its third differences. Binomial transform of 1, 3, 0. - Paul Curtz, Nov 23 2007
MATHEMATICA
LinearRecurrence[{3, -3, 2}, {1, 4, 7}, 40] (* Harvey P. Dale, Apr 27 2015 *)
PROG
(Magma) m:=33; S:=[ [0, 1, 3][ (n-1) mod 3 +1 ]: n in [1..m] ]; T:=[ &+[ Binomial(i-1, k-1)*S[k]: k in [1..i] ]: i in [1..m] ]; [ T[n+1]-T[n]: n in[1..m-1] ]; /* Klaus Brockhaus, Jun 21 2007 */
CROSSREFS
Cf. A130624, A130626 (second differences).
Sequence in context: A083839 A091176 A002974 * A104102 A074705 A352216
KEYWORD
nonn
AUTHOR
Paul Curtz, Jun 18 2007
EXTENSIONS
Edited and extended by Klaus Brockhaus, Jun 21 2007
STATUS
approved