OFFSET
0,2
COMMENTS
Sums of rows of the triangle in A132111.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = A132121(n,3) for n > 2.
G.f.: x*(4+7*x)/(1-x)^4. - Colin Barker, Jun 06 2012
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, Jun 29 2012
a(-n) = -A254407(n-1). - Bruno Berselli, Jan 31 2015
E.g.f.: exp(x)*x*(24 + 45*x + 11*x^2)/6. - Stefano Spezia, Feb 21 2024
MATHEMATICA
CoefficientList[Series[x*(4+7*x)/(1-x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 29 2012 *)
LinearRecurrence[{4, -6, 4, -1}, {0, 4, 23, 68}, 40] (* Harvey P. Dale, Jun 28 2021 *)
PROG
(Magma) I:=[0, 4, 23, 68]; [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
(PARI) a(n)=n*(n+1)*(11*n+1)/6 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Aug 10 2007
STATUS
approved