A075682 First differences of A075681.

0, 2, 19, 39, 61, 86, 114, 145, 179, 216, 256, 299, 345, 394, 446, 501, 559, 620, 684, 751, 821, 894, 970, 1049, 1131, 1216, 1304, 1395, 1489, 1586, 1686, 1789, 1895, 2004, 2116, 2231, 2349, 2470, 2594, 2721, 2851, 2984, 3120, 3259, 3401, 3546

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = (1/2)*(3*n^2 + 17*n - 38), for n > 3. - Ralf Stephan

From G. C. Greubel, Jan 01 2024: (Start)

G.f.: x^2*(2 + 13*x - 12*x^2 + x^3 - x^4)/(1-x)^3.

E.g.f.: (1/2)*(-38 + 20*x + 3*x^2)*exp(x) + 19 + 9*x - x^2 - x^3/3!. (End)

Mathematica

Join[{0, 2, 19}, LinearRecurrence[{3, -3, 1}, {39, 61, 86}, 50]] (* Harvey P. Dale, Aug 26 2014 *)

Prog

(Magma) [0, 2, 19] cat [n*(3*n+17)/2 -19: n in [4..50]]; // G. C. Greubel, Jan 01 2023
(SageMath) [0, 2, 19]+[n*(3*n+17)/2 -19 for n in range(4, 51)] # G. C. Greubel, Jan 01 2024

Crossrefs

Cf. A075681, A075683.

Sequence in context: A240552 A107143 A018610 * A062587 A109946 A141067

Adjacent sequences: A075679 A075680 A075681 * A075683 A075684 A075685

Keyword

nonn

Author

Jon Perry, Oct 12 2002

Extensions

More terms from Ralf Stephan

Status

approved