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

Author

Jon Perry, Oct 12 2002

Keywords

• nonn

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).

Crossrefs

Cf. A075681, A075683.

Programs

Magma

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

Mathematica

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

SageMath

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

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)

Extensions

More terms from Ralf Stephan