A340257 a(n) = 2^n * (1+n*(n+1)/2).

1, 4, 16, 56, 176, 512, 1408, 3712, 9472, 23552, 57344, 137216, 323584, 753664, 1736704, 3964928, 8978432, 20185088, 45088768, 100139008, 221249536, 486539264, 1065353216, 2323644416, 5049942016, 10938744832, 23622320128, 50868518912, 109253230592, 234075717632

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-12,8).

Formula

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

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

a(n) = A000079(n) + A001815(n+1).

a(n) = A000079(n) * A000124(n).

a(n) = 2*a(n-1) + n*2^n = 2*a(n-1) + A036289(n), assuming a(-1) = 1/2.

a(n) = A340298(2^n).

a(n) = 2 * A087431(n) for n > 0.

a(n) = 4 * A007466(n) for n > 0.

Maple

a:= n-> 2^n*(1+n*(n+1)/2):
seq(a(n), n=0..30);

Mathematica

Table[2^n (1+(n(n+1))/2), {n, 0, 30}] (* Harvey P. Dale, Jan 19 2023 *)
(* Alternative: *)
LinearRecurrence[{6, -12, 8}, {1, 4, 16}, 30] (* Harvey P. Dale, Jan 19 2023 *)

Prog

(PARI) a(n)=2^n*(1+n*(n+1)/2) \\ Charles R Greathouse IV, May 28 2026

Crossrefs

Partial sums of A080929.

Cf. A000079, A000124, A001787, A001815, A036289, A087431, A340298, A007466.

Sequence in context: A127393 A239988 A308288 * A261386 A073388 A109634

Adjacent sequences: A340254 A340255 A340256 * A340258 A340259 A340260

Keyword

nonn,easy

Author

Alois P. Heinz, Jan 02 2021

Status

approved