A113829 - OEIS

%I #22 Jan 02 2022 00:32:21

%S 1,9,25,57,185,441,4537,37305,102841,233913,758201,1806777,18583993,

%T 152801721,421237177,958108089,3105591737,7400559033,76120035769,

%U 625875849657,1725387477433,3924410732985,12720503755193,30312689799609

%N a(n) = a(n-1) + 2^(k(n)), where k(n) is the n-th term of the sequence of numbers that are congruent to {0,3,4,5,7,8} mod 12.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,4096,-4096).

%F G.f.: (9+16*x+32*x^2+128*x^3+256*x^4+4096*x^5-4096*x^6)/(1-x-4096*x^6+4096*x^7). - _Charles R Greathouse IV_, Apr 05 2012

%t LinearRecurrence[{1,0,0,0,0,4096,-4096},{1,9,25,57,185,441,4537},30] (* _Harvey P. Dale_, Aug 04 2018 *)

%o (PARI) Vec((-4096*x^6+4096*x^5+256*x^4+128*x^3+32*x^2+16*x+9)/(4096*x^7 - 4096*x^6-x+1)+O(x^99)) \\ _Charles R Greathouse IV_, Apr 05 2012

%Y Cf. A099974, A112627, A080355, A080567, A099969, A099970, A099971, A154571.

%K nonn,easy

%O 1,2

%A _Artur Jasinski_, Jan 27 2006

%E Better definition, corrected offset and edited by _Omar E. Pol_, Jan 08 2009