A081588 Fourth row of the Pascal-(1,4,1) array A081579.

1, 16, 106, 396, 1011, 2076, 3716, 6056, 9221, 13336, 18526, 24916, 32631, 41796, 52536, 64976, 79241, 95456, 113746, 134236, 157051, 182316, 210156, 240696, 274061, 310376, 349766, 392356, 438271, 487636, 540576, 597216, 657681, 722096, 790586, 863276, 940291

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = (6 + 115*n - 150*n^2 + 125*n^3)/6.

G.f.: (1+4*x)^3/(1-x)^4.

From Elmo R. Oliveira, Jun 06 2025: (Start)

E.g.f.: exp(x)*(6 + 90*x + 225*x^2 + 125*x^3)/6.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)

Mathematica

CoefficientList[Series[(1 + 4 x)^3 / (1 - x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Aug 09 2013 *)

Prog

(Magma) [(6+115*n-150*n^2+125*n^3)/6: n in [0..40]]; // Vincenzo Librandi, Aug 09 2013

Crossrefs

Cf. A081579, A081587.

Sequence in context: A146211 A258636 A195806 * A276159 A097762 A297610

Adjacent sequences: A081585 A081586 A081587 * A081589 A081590 A081591

Keyword

easy,nonn

Author

Paul Barry, Mar 23 2003

Status

approved