A081583 Third row of Pascal-(1,2,1) array A081577.

1, 10, 46, 136, 307, 586, 1000, 1576, 2341, 3322, 4546, 6040, 7831, 9946, 12412, 15256, 18505, 22186, 26326, 30952, 36091, 41770, 48016, 54856, 62317, 70426, 79210, 88696, 98911, 109882, 121636, 134200, 147601, 161866, 177022, 193096

Offset

0,2

Comments

Equals binomial transform of [1, 9, 27, 27, 0, 0, 0, ...] where (1, 9, 27, 27) = row 3 of triangle A013610. - Gary W. Adamson, Jul 19 2008

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) = (2 + 9*n + 9*n^3)/2.

G.f.: (1+2*x)^3/(1-x)^4.

a(n) = hypergeommetric2F1([-n, -3], [1], 3). - Peter Luschny, Nov 19 2014

E.g.f.: (1/2)*(2 + 18*x + 27*x^2 + 9*x^3)*exp(x). - G. C. Greubel, May 25 2021

Maple

seq((2+9*n+9*n^3)/2, n=0..40); # G. C. Greubel, May 25 2021

Mathematica

CoefficientList[Series[(1+2x)^3/(1-x)^4, {x, 0, 50}], x] (* Vincenzo Librandi, Aug 09 2013 *)
LinearRecurrence[{4, -6, 4, -1}, {1, 10, 46, 136}, 60] (* Harvey P. Dale, Oct 01 2021 *)

Prog

(Magma) [(2+9*n+9*n^3)/2: n in [0..40]]; // Vincenzo Librandi, Aug 09 2013
(Sage)
a = lambda n: hypergeometric([-n, -3], [1], 3)
[simplify(a(n)) for n in range(36)] # Peter Luschny, Nov 19 2014

Crossrefs

Cf. A013610, A038764, A081584, A081577.

Sequence in context: A248575 A341404 A320697 * A244246 A288117 A213834

Adjacent sequences: A081580 A081581 A081582 * A081584 A081585 A081586

Keyword

easy,nonn

Author

Paul Barry, Mar 23 2003

Status

approved