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A227380
Doubling the first two of every four nonnegative numbers.
2
0, 2, 2, 3, 8, 10, 6, 7, 16, 18, 10, 11, 24, 26, 14, 15, 32, 34, 18, 19, 40, 42, 22, 23, 48, 50, 26, 27, 56, 58, 30, 31, 64, 66, 34, 35, 72, 74, 38, 39, 80, 82, 42, 43, 88, 90, 46, 47, 96, 98, 50, 51, 104, 106, 54, 55, 112, 114
OFFSET
0,2
COMMENTS
a(n) and its differences:
0, 2, 2, 3, 8, 10, 6, 7, 16,...
2, 0, 1, 5, 2, -4, 1, 9, 2,...
-2, 1, 4, -3, -6, 5, 8, -7, -10,... see A103889(n)
3, 3, -7, -3, 11, 3, -15, -3, 19,...
0, -10, 4, 14, -8, -18, 12, 22, -16,...
-10, 14, 10,- 22, -10, 30, 10, -38, -10,... .
The inverse binomial transform is
b(n)=0, 2, -2, 3, 0, -10, 24, -28, 0, 72, -160, 176, 0,...
=(0, 1, -1, 1, 0, -1, 4, -4, 0, 4, -16, 16, 0,...) * a(n).
FORMULA
a(n) = n*A130658(n+2) = 2*A227316(n)/(n+1).
a(n) - a(n-4) = period 4:repeat 8, 8, 4, 4 = 4*A130658(n+2).
G.f.: (x^5 + 5*x^3 - 2*x^2 + 2*x)/((1-x)^2 * (1+x^2)^2). - Ralf Stephan, Jul 13 2013
MATHEMATICA
{2#[[1]], 2#[[2]], #[[3]], #[[4]]}&/@Partition[Range[0, 60], 4]//Flatten (* or *) LinearRecurrence[{2, -3, 4, -3, 2, -1}, {0, 2, 2, 3, 8, 10}, 60] (* Harvey P. Dale, Dec 14 2021 *)
CROSSREFS
Cf. A001477.
Sequence in context: A300354 A091681 A076541 * A159789 A153932 A158763
KEYWORD
nonn,easy,changed
AUTHOR
Paul Curtz, Jul 09 2013
STATUS
approved