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

1,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (2,-1).

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)

Mathematica

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

Prog

(Magma) [2, 17, 20] cat [3*n+10: n in [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

Crossrefs

Cf. A075681, A075682.

Sequence in context: A240475 A107139 A042055 * A340044 A309055 A157191

Adjacent sequences: A075680 A075681 A075682 * A075684 A075685 A075686

Keyword

nonn

Author

Jon Perry, Oct 12 2002

Extensions

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

Status

approved