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 A201630 a(n) = a(n-1)+2*a(n-2) with n>1, a(0)=2, a(1)=7. 4
 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 (list; graph; refs; listen; history; text; internal format)
 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) = 2*sum(a(i), i=0..n-2)+7 for n>1. a(n) = A097581(A042948(n+1)). a(n+2)-a(n) = a(n+1)+a(n) = A005010(n). 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); CROSSREFS Cf. A001045. 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

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Last modified September 27 13:42 EDT 2023. Contains 365694 sequences. (Running on oeis4.)