A139545 Binomial transform of [1, 0, 0, 4, 0, 0, 7, 0, 0, 10, ...].

1, 1, 1, 5, 17, 41, 88, 190, 421, 935, 2051, 4445, 9562, 20476, 43681, 92837, 196613, 415073, 873820, 1835002, 3844765, 8039075, 16777223, 34952549, 72701278, 150994936, 313174681, 648719009, 1342177289, 2773833065, 5726623072

Offset

1,4

Links

Table of n, a(n) for n=1..31.

Formula

A007318 * [1, 0, 0, 4, 0, 0, 7, 0, 0, 10, ...].

a(n) = Sum_{k=0..n/3} (3k+1)*binomial(n,3k). - Emeric Deutsch, May 03 2008

G.f.: x*(1 - 3x + 3x^2 + x^3)*(1-x)^2/((1-2x)^2*(1-x+x^2)^2). - R. J. Mathar, Nov 25 2008

Example

a(4) = 5 = (1, 3, 3, 1) dot (1, 0, 0, 4) = (1 + 0 + 0 + 4).

Maple

a:=proc(n) options operator, arrow: sum((3*k+1)*binomial(n, 3*k), k=0..(1/3)*n) end proc: seq(a(n), n=0..30); # Emeric Deutsch, May 03 2008

Crossrefs

Sequence in context: A109722 A097121 A007904 * A106972 A086499 A097123

Adjacent sequences: A139542 A139543 A139544 * A139546 A139547 A139548

Keyword

nonn

Author

Gary W. Adamson, Apr 26 2008

Extensions

More terms from Emeric Deutsch, May 03 2008

Status

approved