The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A136395 Binomial transform of [1, 3, 4, 3, 2, 0, 0, 0,...]. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 30 19:28 EDT 2020. Contains 333127 sequences. (Running on oeis4.)