A201630 a(n) = a(n-1) + 2*a(n-2) with n>1, a(0)=2, a(1)=7.

2, 7, 11, 25, 47, 97, 191, 385, 767, 1537, 3071, 6145, 12287, 24577, 49151, 98305, 196607, 393217, 786431, 1572865, 3145727, 6291457, 12582911, 25165825, 50331647, 100663297, 201326591, 402653185, 805306367, 1610612737, 3221225471, 6442450945, 12884901887

Offset

0,1

References

B. Satyanarayana and K. S. Prasad, Discrete Mathematics and Graph Theory, PHI Learning Pvt. Ltd. (Eastern Economy Edition), 2009, p. 73 (problem 3.3).

Links

Bruno Berselli, Table of n, a(n) for n = 0..1000

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

Formula

G.f.: (2+5*x)/((1+x)*(1-2*x)).

a(n) = 3*2^n - (-1)^n.

a(n) = 7 + 2*Sum_{i=0..n-2} a(i), for n>0.

a(n) = A097581(A042948(n+1)).

a(n+2) - a(n) = a(n+1) + a(n) = A005010(n).

E.g.f.: 3*exp(2*x) - exp(-x). - G. C. Greubel, Feb 07 2025

Mathematica

LinearRecurrence[{1, 2}, {2, 7}, 33]

Prog

(PARI) v=vector(33); v[1]=2; v[2]=7; for(i=3, #v, v[i]=v[i-1]+2*v[i-2]); v
(Magma) [n le 2 select 5*n-3 else Self(n-1)+2*Self(n-2): n in [1..33]];
(Maxima) a[0]:2$ a[1]:7$ a[n]:=a[n-1]+2*a[n-2]$ makelist(a[n], n, 0, 32);
(SageMath)
def A201630(n): return 3*2**n - (-1)**n
print([A201630(n) for n in range(31)]) # G. C. Greubel, Feb 07 2025

Crossrefs

Cf. A001045, A005010, A042948, A097581.

Sequence in context: A235355 A103184 A093039 * A023862 A024479 A295138

Adjacent sequences: A201627 A201628 A201629 * A201631 A201632 A201633

Keyword

nonn,easy

Author

Bruno Berselli, Dec 03 2011

Status

approved