A387939 a(n) = 2^n*(n^2/4+n/4+4) - Fibonacci(n+4).

1, 4, 14, 43, 123, 334, 873, 2215, 5488, 13335, 31879, 75166, 175141, 403907, 923112, 2092971, 4711827, 10540350, 23444177, 51875855, 114248416, 250534639, 547235279, 1190985918, 2583373453, 5586298699, 12045209048, 25902675235, 55563961083, 118913382430, 253934238489, 541156651831, 1151036304976

Offset

0,2

Links

Table of n, a(n) for n=0..32.

Kamilla Oliver and Helmut Prodinger, Summations in Bernoulli's triangles via generating functions, J. Int. Seq. 20 (2017) #17.1.3., m=4.

Index entries for linear recurrences with constant coefficients, signature (7,-17,14,4,-8).

Formula

Convolution of A011782 and A079282.

G.f.: (1-x)^3 / ( (1-x^2-x)*(1-2*x)^3 ).

Maple

seq( -combinat[fibonacci](n+4)+(n^2/4+n/4+4)*2^n, n=0..40) ;

Mathematica

a[n_]:=2^n*(n^2/4+n/4+4) - Fibonacci[n+4]; Array[a, 33, 0] (* James C. McMahon, Oct 29 2025 *)
(* Alternative: *)
CoefficientList[Series[(1-x)^3 / ( (1-x^2-x)*(1-2*x)^3 ), {x, 0, 32}], x] (* James C. McMahon, Oct 29 2025 *)
(* Alternative: *)
LinearRecurrence[{7, -17, 14, 4, -8}, {1, 4, 14, 43, 123}, 33] (* James C. McMahon, Oct 29 2025 *)

Crossrefs

Cf. A079282.

Sequence in context: A135483 A095377 A296253 * A247470 A049539 A037528

Adjacent sequences: A387936 A387937 A387938 * A387940 A387941 A387942

Keyword

nonn,easy,changed

Author

R. J. Mathar, Oct 29 2025

Status

approved