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A181407 a(n) = (n-4)*(n-3)*2^(n-2). 3
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 (list; graph; refs; listen; history; text; internal format)
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.

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).

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

Cf. A176027, A181318.

Sequence in context: A053375 A117252 A332498 * A114187 A016037 A106449

Adjacent sequences:  A181404 A181405 A181406 * A181408 A181409 A181410

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Jan 28 2011

STATUS

approved

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Last modified May 31 02:51 EDT 2020. Contains 334747 sequences. (Running on oeis4.)