A081910 a(n) = 4^n*(n^2-n+32)/32.

1, 4, 17, 76, 352, 1664, 7936, 37888, 180224, 851968, 3997696, 18612224, 85983232, 394264576, 1795162112, 8120172544, 36507222016, 163208757248, 725849473024, 3212635537408, 14156212207616, 62122406969344, 271579372060672

Offset: 0

Author

Paul Barry, Mar 31 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A081909 4th binomial transform of (1,0,1,0,0,0,......). Case k=4 where a(n,k)=k^n(n^2-n+2k^2)/(2k^2) with G.f.: (1-2kx+(k^2+1)x^2)/(1-kx)^3.

Links

• Vincenzo Librandi and Harvey P. Dale, Table of n, a(n) for n = 0..1000 [First 168 terms from _Vincenzo Librandi_]
• Index entries for linear recurrences with constant coefficients, signature (12,-48,64).

Crossrefs

Cf. A081911.

Programs

Magma

[4^n*(n^2-n+32)/32: n in [0..40]]; // Vincenzo Librandi, Apr 27 2011

Maple

A081910:=n->4^n*(n^2-n+32)/32; seq(A081910(n), n=0..30); # Wesley Ivan Hurt, Mar 12 2014

Mathematica

Table[(4^n (n^2 - n + 32))/32, {n, 0, 30}] (* or *) LinearRecurrence[{12, -48, 64}, {1, 4, 17}, 30] (* Harvey P. Dale, Jan 18 2014 *)
CoefficientList[Series[(1 - 8 x + 17 x^2)/(1 - 4 x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 14 2014 *)

PARI

a(n) = 4^n*(n^2-n+32)/32; \\ Joerg Arndt, Mar 12 2014

Formula

a(n) = 4^n*(n^2-n+32)/32.

G.f.: (1-8*x+17*x^2)/(1-4*x)^3.

a(0)=1, a(1)=4, a(2)=17, a(n)=12*a(n-1)-48*a(n-2)+64*a(n-3). - Harvey P. Dale, Jan 18 2014