A271114 Expansion of (1+x)*(2+x)/(1-x)^2.

2, 7, 13, 19, 25, 31, 37, 43, 49, 55, 61, 67, 73, 79, 85, 91, 97, 103, 109, 115, 121, 127, 133, 139, 145, 151, 157, 163, 169, 175, 181, 187, 193, 199, 205, 211, 217, 223, 229, 235, 241, 247, 253, 259, 265, 271, 277, 283, 289, 295, 301, 307, 313, 319, 325

Offset: 0

Author

Colin Barker, Mar 31 2016

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A016921, A270700.

Cf. A016969, A082369, A100764, A128470, A132231, A156376.

Programs

Mathematica

Join[{2}, LinearRecurrence[{2, -1}, {7, 13}, 100]] (* G. C. Greubel, Mar 31 2016 *)

PARI

Vec((1+x)*(2+x)/(1-x)^2 + O(x^70))

Formula

G.f.: (1+x)*(2+x)/(1-x)^2.

a(n) = A270700(n)/6.

a(n) = 6*n+1 = A016921(n) for n>0.

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

E.g.f.: 1 + (1+6*x)*exp(x). - G. C. Greubel, Mar 31 2016

From Bruno Berselli and G. C. Greubel, Mar 31 2016: (Start)

a(5*m+1) = 30*m + 7 = A132231(m+1).

a(5*m+2) = 30*m + 13 = A082369(m+1).

a(5*m+3) = 30*m + 19 = A156376(m).

a(5*m+4) = 30*m + 25 = 5*A016969(m).

a(5*m+5) = 30*m + 31 = A128470(m+1). (End)

a(n) = A100764(n+3) for n >= 1. - Georg Fischer, Oct 30 2018