A075683 2nd differences of A075681.

2, 17, 20, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94, 97, 100, 103, 106, 109, 112, 115, 118, 121, 124, 127, 130, 133, 136, 139, 142, 145, 148, 151, 154, 157, 160, 163, 166, 169, 172, 175, 178, 181, 184, 187, 190, 193, 196

Offset: 1

Author

Jon Perry, Oct 12 2002

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A075681, A075682.

Programs

Magma

[2,17,20] cat [3*n+10: n in [4..70]]; // G. C. Greubel, Jan 02 2024

Mathematica

Join[{2,17,20}, 10+3*Range[4,70]] (* G. C. Greubel, Jan 02 2024 *)

SageMath

[2,17,20]+[3*n+10 for n in range(4,71)] # G. C. Greubel, Jan 02 2024

Formula

From G. C. Greubel, Jan 02 2024: (Start)

a(n) = 2*a(n-1) - a(n-2), for n >= 6.

a(n) = A075681(n+2) - 2*A075681(n+1) + A075681(n).

a(n) = A075682(n+1) - A075682(n).

a(n) = 3*n + 10 - 11*[n=1] + [n=2] + [n=3].

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

E.g.f.: (10 + 3*x)*exp(x) - 10 - 11*x + x^2/2! + x^3/3!. (End)

Extensions

Terms a(11) onward added by G. C. Greubel, Jan 02 2024