OFFSET
0,1
COMMENTS
Binomial transform of (3, 0, -1, followed by A005563).
The sequence and its successive differences are:
3, 3, 2, 0, 0, 16, 96, 384, a(n),
0, -1, -2, 0, 16, 80, 288, 896, A178987,
-1, -1, 2, 16, 64, 208, 608, 2688, -A127276,
0, 3, 14, 48, 144, 400, 1056, 2688, A176027,
3, 11, 34, 96, 256, 656, 1632, 3968, A084266(n+1)
8, 23, 62, 160, 400, 976, 2336, 5504,
15, 39, 98, 240, 576, 1360, 3168, 7296.
Division of the k-th column by abs(A174882(k)) gives
3, 3, 1, 0, 0, 1, 3, 3, 5, 15, 21, 14, A064038(n-3),
0, -1, -1, 0, 1, 5, 9, 7, 10, 27, 35, 22, A160050(n-3),
-1, -1, 1, 2, 4, 13, 19, 13, 17, 43, 53, 32, A176126,
0, 3, 7, 6, 9, 25, 33, 21, 26, 63, 75, 44, A178242,
3, 11, 17, 12, 16, 41, 51, 31, 37, 87, 101, 58,
8 23, 31, 20, 25, 61, 73, 43, 50, 115, 131, 74,
15, 39, 49, 30, 36, 85, 99, 57, 65, 147, 165, 92.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-12,8).
FORMULA
a(n) = 16*A001788(n-4).
a(n+1) - a(n) = A178987(n).
G.f.: (3 - 15*x + 20*x^2) / (1-2*x)^3. - R. J. Mathar, Jan 30 2011
E.g.f.: (x^2 - 3*x + 3)*exp(2*x). - G. C. Greubel, Feb 21 2019
MATHEMATICA
Table[(n-4)*(n-3)*2^(n-2), {n, 0, 40}] (* G. C. Greubel, Feb 21 2019 *)
PROG
(Magma) [(n-4)*(n-3)*2^(n-2): n in [0..40] ]; // Vincenzo Librandi, Feb 01 2011
(PARI) vector(40, n, n--; (n-4)*(n-3)*2^(n-2)) \\ G. C. Greubel, Feb 21 2019
(Sage) [(n-4)*(n-3)*2^(n-2) for n in (0..40)] # G. C. Greubel, Feb 21 2019
(GAP) List([0..40], n-> (n-4)*(n-3)*2^(n-2)); # G. C. Greubel, Feb 21 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Jan 28 2011
STATUS
approved