A136395 Binomial transform of [1, 3, 4, 3, 2, 0, 0, 0, ...].

1, 4, 11, 25, 51, 96, 169, 281, 445, 676, 991, 1409, 1951, 2640, 3501, 4561, 5849, 7396, 9235, 11401, 13931, 16864, 20241, 24105, 28501, 33476, 39079, 45361, 52375, 60176, 68821, 78369, 88881, 100420, 113051, 126841, 141859, 158176, 175865, 195001

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

A007318 * [1, 3, 4, 3, 2, 0, 0, 0, ...]. A001263 * [1, 3, 1, 0, 0, 0, ...]

O.g.f.: -(1-x+x^2+x^4)/(-1+x)^5. - R. J. Mathar, Apr 02 2008

Example

a(3) = 25 = (1, 3, 3, 1) dot (1, 3, 4, 3) = (1 + 9 + 12 + 3).
a(3) = 25 = (1, 6, 6, 1) dot (1, 3, 1, 0) = (1 + 18 + 6 + 0), where (1, 6, 6, 1) = row 4 of the Narayana triangle, A001263.

Maple

a := n-> (Matrix([[11, 4, 1, 1, 5]]). Matrix(5, (i, j)-> if (i=j-1) then 1 elif j=1 then [5, -10, 10, -5, 1][i] else 0 fi)^n)[1, 3]; seq (a(n), n=0..50); # Alois P. Heinz, Aug 14 2008

Mathematica

CoefficientList[Series[-(1-x+x^2+x^4)/(-1+x)^5, {x, 0, 40}], x] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {1, 4, 11, 25, 51}, 40] (* Harvey P. Dale, Dec 27 2016 *)

Crossrefs

Cf. A001263.

Sequence in context: A215052 A011851 A193912 * A014160 A014162 A014169

Adjacent sequences: A136392 A136393 A136394 * A136396 A136397 A136398

Keyword

nonn,easy

Author

Gary W. Adamson, Dec 29 2007

Extensions

More terms from R. J. Mathar, Apr 02 2008

More terms from Alois P. Heinz, Aug 14 2008

Status

approved