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A168673
Binomial transform of A169609.
2
1, 4, 10, 20, 38, 74, 148, 298, 598, 1196, 2390, 4778, 9556, 19114, 38230, 76460, 152918, 305834, 611668, 1223338, 2446678, 4893356, 9786710, 19573418, 39146836, 78293674, 156587350, 313174700, 626349398, 1252698794, 2505397588, 5010795178, 10021590358
OFFSET
0,2
COMMENTS
Sequence and successive differences are identical to their third differences. See principal sequence A024495. Main diagonal of the array of successive differences is A083595 (1,6,8,20,36,...).
FORMULA
a(n+1) - 2a(n) = A130772(n).
a(n) = A062092(n) - A130151(n+1).
a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) for n > 2; a(0) = 1, a(1) = 4, a(2) = 10.
G.f.: (1 + x + x^2)/(1 -3*x +3*x^2 -2*x^3). - Philippe Deléham, Dec 03 2009
MATHEMATICA
LinearRecurrence[{3, -3, 2}, {1, 4, 10}, 25] (* G. C. Greubel, Jul 29 2016 *)
RecurrenceTable[{a[0] == 1, a[1] == 4, a[2] == 10, a[n] == 3 a[n-1] - 3 a[n-2] + 2 a[n-3]}, a, {n, 40}] (* Vincenzo Librandi, Jul 30 2016 *)
PROG
(Magma) I:=[1, 4, 10]; [n le 3 select I[n] else 3*Self(n-1)- 3*Self(n-2)+2*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jul 30 2016
(PARI) a(n)=([0, 1, 0; 0, 0, 1; 2, -3, 3]^n*[1; 4; 10])[1, 1] \\ Charles R Greathouse IV, Jul 30 2016
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Dec 02 2009
EXTENSIONS
Edited and extended by Klaus Brockhaus, Dec 03 2009
STATUS
approved