OFFSET
1,2
COMMENTS
Row 1 of the convolution array A213838. - Clark Kimberling, Jul 05 2012
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = (1/6)*(8*n^3 - 6*n^2 + 4*n).
G.f.: x*(1+4*x+3*x^2)/(1-4*x+6*x^2-4*x^3+x^4). - Colin Barker, Jan 04 2012
From Elmo R. Oliveira, Aug 28 2025: (Start)
E.g.f.: exp(x)*x*(4*x^2 + 9*x + 3)/3.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 4.
MATHEMATICA
LinearRecurrence[{4, -6, 4, -1}, {1, 8, 29, 72}, 50] (* Paolo Xausa, Aug 06 2025 *)
PROG
(Magma) [(1/6)*(8*n^3-6*n^2+4*n): n in [1..40]]; // Vincenzo Librandi, Aug 03 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
James A. Record (james.record(AT)gmail.com), Nov 07 2004
STATUS
approved
