A061982 a(n) = 3^n - (n+1)*(n+2)/2.

0, 0, 3, 17, 66, 222, 701, 2151, 6516, 19628, 58983, 177069, 531350, 1594218, 4782849, 14348771, 43046568, 129139992, 387420299, 1162261257, 3486784170, 10460352950, 31381059333, 94143178527, 282429536156, 847288609092, 2541865827951, 7625597484581, 22876792454526

Offset

0,3

Links

Harry J. Smith, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (6,-12,10,-3).

Formula

From G. C. Greubel, Jun 13 2022: (Start)

a(n) = 3^n - binomial(n+2, 2).

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

E.g.f.: exp(3*x) - (1/2)*(2 + 4*x + x^2)*exp(x). (End)

Mathematica

LinearRecurrence[{6, -12, 10, -3}, {0, 0, 3, 17}, 40] (* G. C. Greubel, Jun 13 2022 *)

Prog

(PARI) a(n) = { 3^n - (n + 1)*(n + 2)/2 } \\ Harry J. Smith, Jul 29 2009
(Magma) [3^n -Binomial(n+2, 2): n in [0..40]]; // G. C. Greubel, Jun 13 2022
(SageMath) [3^n -binomial(n+2, 2) for n in (0..40)] # G. C. Greubel, Jun 13 2022

Crossrefs

Column of A061980.

Cf. A000217, A000244.

Sequence in context: A174285 A227427 A120386 * A101562 A396388 A034566

Adjacent sequences: A061979 A061980 A061981 * A061983 A061984 A061985

Keyword

nonn,easy

Author

Henry Bottomley, May 24 2001

Status

approved