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A168207
a(n) = 5*n - a(n-1) + 1 with n>1, a(1)=2.
1
2, 14, 7, 19, 12, 24, 17, 29, 22, 34, 27, 39, 32, 44, 37, 49, 42, 54, 47, 59, 52, 64, 57, 69, 62, 74, 67, 79, 72, 84, 77, 89, 82, 94, 87, 99, 92, 104, 97, 109, 102, 114, 107, 119, 112, 124, 117, 129, 122, 134, 127, 139, 132, 144, 137, 149, 142, 154, 147, 159, 152, 164
OFFSET
1,1
FORMULA
a(n) = (10*n + 17 + 19*(-1)^n)/4. - Jon E. Schoenfield, Jun 24 2010
G.f.: x*(2+12*x-9*x^2)/((1+x)*(1-x)^2). - Bruno Berselli, Feb 28 2012
E.g.f.: (1/4)*(19 - 36*exp(x) + (17 + 10*x)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 15 2016
Sum_{n>=1} (-1)^(n+1)/a(n) = 13/36 + sqrt((5+sqrt(5))/10)*Pi/5 - log(phi)/sqrt(5), where phi is the golden ratio (A001622). - Amiram Eldar, Feb 23 2023
MATHEMATICA
LinearRecurrence[{1, 1, -1}, {2, 14, 7}, 30] (* Vincenzo Librandi, Feb 28 2012 *)
PROG
(Magma) I:=[2, 14, 7]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..60]]; // Vincenzo Librandi, Feb 28 2012
CROSSREFS
Cf. A001622.
Sequence in context: A344115 A373790 A191995 * A082609 A271382 A158787
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Nov 20 2009
STATUS
approved