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
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).
Programs
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Magma
[3^n -Binomial(n+2,2): n in [0..40]]; // G. C. Greubel, Jun 13 2022
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Mathematica
LinearRecurrence[{6,-12,10,-3}, {0,0,3,17}, 40] (* G. C. Greubel, Jun 13 2022 *) -
PARI
a(n) = { 3^n - (n + 1)*(n + 2)/2 } \\ Harry J. Smith, Jul 29 2009 -
SageMath
[3^n -binomial(n+2,2) for n in (0..40)] # G. C. Greubel, Jun 13 2022
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)