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A141478 Binomial(n+2,3)*4^3. 2
64, 256, 640, 1280, 2240, 3584, 5376, 7680, 10560, 14080, 18304, 23296, 29120, 35840, 43520, 52224, 62016, 72960, 85120, 98560, 113344, 129536, 147200, 166400, 187200, 209664, 233856, 259840, 287680, 317440, 349184, 382976, 418880, 456960 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Number of n permutations (n>=3) of 5 objects u, v, z, x, y with repetition allowed, containing n-3 u's. Example:

if n=3 then n-3 =zero (0) u, a(1)=64

if n=4 then n-3= one (1) u, a(2)=256

if n=5 then n-3= two (2) u, a(3)=640

etc...

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

G.f.:64*x/(1-x)^4. a(n)=32*n*(n+1)*(n+2)/3 = 64*A000292(n).

a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). - Vincenzo Librandi, Jun 29 2012

MAPLE

seq(binomial(n+2, 3)*4^3, n=1..36);

MATHEMATICA

CoefficientList[Series[64/(1-x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 29 2012 *)

PROG

(MAGMA) [Binomial(n+2, 3)*4^3: n in [1..34]];  // Bruno Berselli, Apr 07 2011

(MAGMA) I:=[64, 256, 640, 1280]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Jun 29 2012

CROSSREFS

Cf. A035008, A038231 (3rd subdiagonal).

Sequence in context: A236331 A321070 A017066 * A107262 A255662 A045029

Adjacent sequences:  A141475 A141476 A141477 * A141479 A141480 A141481

KEYWORD

nonn,easy

AUTHOR

Zerinvary Lajos, Aug 09 2008

EXTENSIONS

Offset adapted to the g.f and indexes in comment by Bruno Berselli, Apr 07 2011

STATUS

approved

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Last modified December 3 05:05 EST 2021. Contains 349445 sequences. (Running on oeis4.)