A081912 a(n) = 6^n*(n^2 - n + 72)/72.

1, 6, 37, 234, 1512, 9936, 66096, 443232, 2985984, 20155392, 136048896, 917070336, 6167549952, 41358864384, 276451356672, 1841557856256, 12224809598976, 80871817347072, 533189772509184, 3503818505060352, 22952550207062016, 149902496042582016, 976194303496814592

Offset

0,2

Comments

Binomial transform of A081911 6th binomial transform of (1,0,1,0,0,0,...). Case k=6 where a(n,k) = k^n*(n^2 - n + 2*k^2)/(2*k^2) with g.f. (1 - 2*k*x + (k^2+1)*x^2)/(1-k*x)^3.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..150

Index entries for linear recurrences with constant coefficients, signature (18,-108,216).

Formula

a(n) = 6^n*(n^2 - n + 72)/72.

G.f.: (1 - 12*x + 37*x^2)/(1-6*x)^3.

From Elmo R. Oliveira, Nov 12 2025: (Start)

E.g.f.: (1 + x^2/2)*exp(6*x).

a(n) = 18*a(n-1) - 108*a(n-2) + 216*a(n-3). (End)

Prog

(Magma) [6^n*(n^2-n+72)/72: n in [0..40]]; // Vincenzo Librandi, Apr 27 2011

Crossrefs

Cf. A081911.

Sequence in context: A081570 A122898 A317629 * A081188 A218186 A154623

Adjacent sequences: A081909 A081910 A081911 * A081913 A081914 A081915

Keyword

easy,nonn

Author

Paul Barry, Mar 31 2003

Status

approved