A023545 Convolution of natural numbers >= 2 and natural numbers >= 3.

6, 17, 34, 58, 90, 131, 182, 244, 318, 405, 506, 622, 754, 903, 1070, 1256, 1462, 1689, 1938, 2210, 2506, 2827, 3174, 3548, 3950, 4381, 4842, 5334, 5858, 6415, 7006, 7632, 8294, 8993, 9730, 10506, 11322, 12179, 13078, 14020, 15006, 16037, 17114, 18238, 19410, 20631

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

László Németh, Tetrahedron trinomial coefficient transform, arXiv:1905.13475 [math.CO], 2019.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = n*(n^2 + 12*n + 23)/6. - Ralf Stephan, Feb 15 2004; corrected by Lucas Sidiropoulos (lsid77(AT)yahoo.com), Jun 23 2008

From Colin Barker, Jun 20 2012: (Start)

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).

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

E.g.f.: exp(x)*x*(36 + 15*x + x^2)/6. - Stefano Spezia, Mar 28 2023

Mathematica

CoefficientList[Series[(2-x)*(3-2*x)/(1-x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 29 2012 *)
LinearRecurrence[{4, -6, 4, -1}, {6, 17, 34, 58}, 50] (* Harvey P. Dale, Aug 10 2014 *)

Prog

(Magma) I:=[6, 17, 34, 58]; [n le 4 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, Jun 29 2012

Crossrefs

Sequence in context: A066486 A301719 A056109 * A038633 A083045 A012277

Adjacent sequences: A023542 A023543 A023544 * A023546 A023547 A023548

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved