A093380 -id:A093380 - cp's OEIS frontend

A093381 Expansion of (1 - 2x - 3x^2 - 4x^3)/((1-x)(1-2x)(1-3x)(1-4*x)).

1, 8, 42, 186, 766, 3058, 12062, 47426, 186606, 735858, 2909182, 11528866, 45781646, 182104658, 725311902, 2891845506, 11539011886, 46070609458, 184025468222, 735329653346, 2938999333326, 11749034250258, 46975237266142

Offset: 0

Paul Barry, Apr 28 2004

Second binomial transform of A093380.

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (10,-35,50,-24).

Cf. A033484.

[4/3-5*2^n+2*3^n+8*4^n/3: n in [0..30]]; // Vincenzo Librandi, May 31 2011

CoefficientList[Series[(1-2x-3x^2-4x^3)/((1-x)(1-2x)(1-3x)(1-4x)),{x,0,30}],x] (* or *) LinearRecurrence[{10,-35,50,-24},{1,8,42,186},30] (* Harvey P. Dale, May 29 2013 *)

a(n) = 4/3 - 5*2^n + 2*3^n + 8*4^n/3;
a(n) = 2*A000244(n) - 5*A000079(n) + 4*A001045(2n+1).
a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4), n > 3. - Harvey P. Dale, May 29 2013

A173197 a(0)=1, a(n)= 2+2^n/6+4*(-1)^n/3, n>0.

Original entry on oeis.org

1, 1, 4, 2, 6, 6, 14, 22, 46, 86, 174, 342, 686, 1366, 2734, 5462, 10926, 21846, 43694, 87382, 174766, 349526, 699054, 1398102, 2796206, 5592406, 11184814, 22369622, 44739246, 89478486, 178956974, 357913942, 715827886, 1431655766, 2863311534, 5726623062, 11453246126, 22906492246, 45812984494, 91625968982, 183251937966, 366503875926, 733007751854

Offset: 0

Paul Curtz, Feb 12 2010

Linked to Jacobsthal numbers (expansion of tan(x), a.k.a. Zag numbers) A000182=1,2,16,272,...: a(n+1)-2a(n) = -(-1)^n*(A000182(n) mod 10) = (-1,2,-6,2,-6,2,-6,...).
Cf. A173114, related to Euler (or secant, or Zig) numbers, A000364. a(n+1)+A010684=A001045.
First differences: 0,3,-2,4,0,8,8,24,... = 0,A154879 (third differences of A001045).
Main diagonal: A003945; first upper diagonal: -A171449; second: 4*A011782.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,1,-2).

a(n) = A093380(n+4), n>3.
a(n) = +2*a(n-1) +a(n-2) -2*a(n-3), n>3.
G.f.: 1-x*(-1-2*x+7*x^2)/((x-1)*(2*x-1)*(1+x)).
a(2n+2)+a(2n+3)=6*A047689.
a(2n)-a(2n-2) = 3,1,2,4,8,16,... = 3,A000079.

cp's OEIS Frontend

A093381 Expansion of (1 - 2x - 3x^2 - 4x^3)/((1-x)(1-2x)(1-3x)(1-4*x)).

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A173197 a(0)=1, a(n)= 2+2^n/6+4*(-1)^n/3, n>0.

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cp's OEIS Frontend

A093381 Expansion of (1 - 2*x - 3*x^2 - 4*x^3)/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)).

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A173197 a(0)=1, a(n)= 2+2^n/6+4*(-1)^n/3, n>0.

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A093381 Expansion of (1 - 2x - 3x^2 - 4x^3)/((1-x)(1-2x)(1-3x)(1-4*x)).