A179905 (1, 4, 7, 10, 13, ...) convolved with (1, 0, 4, 7, 10, 13, ...); given A016777 = (1, 4, 7, 10, 13, ...).

1, 4, 11, 33, 79, 158, 279, 451, 683, 984, 1363, 1829, 2391, 3058, 3839, 4743, 5779, 6956, 8283, 9769, 11423, 13254, 15271, 17483, 19899, 22528, 25379, 28461, 31783, 35354, 39183, 43279, 47651, 52308, 57259, 62513, 68079, 73966

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

(1 + 4x + 11x^2 + 33x^3 + ...) = (1 + 4x + 10x^2 + 13x^3 + ...) *

(1 + 4x^2 + 10x^3 + 13x^4 + ...).

G.f. 1 -x*(x-4)*(3*x^2-x+1)/(x-1)^4. - R. J. Mathar, Apr 04 2012

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, Jul 04 2012

Example

a(4) = 79 = (13, 10, 7, 4, 1) dot (1, 0, 4, 7, 10) = (13 + 0 + 28 + 28 + 10).

Mathematica

CoefficientList[Series[1-x*(x-4)*(3*x^2-x+1)/(x-1)^4, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 04 2012 *)
Join[{1}, LinearRecurrence[{4, -6, 4, -1}, {4, 11, 33, 79}, 40]] (* Harvey P. Dale, Jun 24 2014 *)

Prog

(Magma) I:=[1, 4, 11, 33, 79]; [n le 5 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, Jul 04 2012

Crossrefs

Cf. A016777.

Sequence in context: A149232 A149233 A273038 * A034745 A217860 A307073

Adjacent sequences: A179902 A179903 A179904 * A179906 A179907 A179908

Keyword

nonn,easy

Author

Gary W. Adamson, Jul 31 2010

Status

approved