A181407 a(n) = (n-4)*(n-3)*2^(n-2).

3, 3, 2, 0, 0, 16, 96, 384, 1280, 3840, 10752, 28672, 73728, 184320, 450560, 1081344, 2555904, 5963776, 13762560, 31457280, 71303168, 160432128, 358612992, 796917760, 1761607680, 3875536896, 8489271296, 18522046464, 40265318400, 87241523200, 188441690112

Offset: 0

Author

Paul Curtz, Jan 28 2011

Keywords

• nonn
• easy

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.

Columns are (or from) A005563, A142463, A056220, A002378, A000290, A001844, A058331, A002061, A002522, A097080, A093328, A014206.

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).

Crossrefs

Cf. A176027, A181318.

Programs

GAP

List([0..40], n-> (n-4)*(n-3)*2^(n-2)); # G. C. Greubel, Feb 21 2019

Magma

[(n-4)*(n-3)*2^(n-2): n in [0..40] ]; // Vincenzo Librandi, Feb 01 2011

Mathematica

Table[(n-4)*(n-3)*2^(n-2), {n,0,40}] (* G. C. Greubel, Feb 21 2019 *)

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

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