A097810 a(n) = 7*2^n - 3*n - 6.

1, 5, 16, 41, 94, 203, 424, 869, 1762, 3551, 7132, 14297, 28630, 57299, 114640, 229325, 458698, 917447, 1834948, 3669953, 7339966, 14679995, 29360056, 58720181, 117440434, 234880943, 469761964, 939524009, 1879048102, 3758096291

Offset: 0

Author

Paul Barry, Aug 25 2004

Keywords

• easy
• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

Crossrefs

Cf. A079583, A097809, A131068.

Programs

Mathematica

s=1;lst={s};Do[s+=(s+=n)+n++;AppendTo[lst, s], {n, 1, 5!, 1}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 15 2008 *)
Table[7*2^n-3n-6,{n,0,30}] (* or *) LinearRecurrence[{4,-5,2},{1,5,16},30] (* Harvey P. Dale, Nov 15 2011 *)

Formula

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

a(n) = 2*a(n-1) + 3*n, n > 0, a(0)=1.

a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3).

From Elmo R. Oliveira, Mar 06 2025: (Start)

E.g.f.: exp(x)*(7*exp(x) - 3*(x + 2)).

a(n) = A131068(n+1)/2. (End)