|
|
A023545
|
|
Convolution of natural numbers >= 2 and natural numbers >= 3.
|
|
1
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
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
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)
|
|
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
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|