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A075682
First differences of A075681.
2
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
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
Sequence in context: A240552 A107143 A018610 * A062587 A109946 A141067
KEYWORD
nonn
AUTHOR
Jon Perry, Oct 12 2002
EXTENSIONS
More terms from Ralf Stephan
STATUS
approved