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A100532 The first four numbers of this sequence are the primes 2,3,5,7. The other terms are calculated by adding the previous four terms.

%I A100532 #21 Jul 07 2022 02:19:59
%S A100532 2,3,5,7,17,32,61,117,227,437,842,1623,3129,6031,11625,22408,43193,
%T A100532 83257,160483,309341,596274,1149355,2215453,4270423,8231505,15866736,
%U A100532 30584117,58952781,113635139,219038773,422210810,813837503,1568722225,3023809311,5828579849
%N A100532 The first four numbers of this sequence are the primes 2,3,5,7. The other terms are calculated by adding the previous four terms.
%H A100532 Martin Burtscher, Igor Szczyrba, and Rafał Szczyrba, <a href="https://www.emis.de/journals/JIS/VOL18/Szczyrba/sz3.html">Analytic Representations of the n-anacci Constants and Generalizations Thereof</a>, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.
%H A100532 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,1).
%F A100532 a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) where n >= 5 and a(1) = 2, a(2) = 3, a(3) = 5 and a(4) = 7.
%F A100532 G.f.:  x*(1-x)*(2+3*x+3*x^2) / ( 1-x-x^2-x^3-x^4 ). - _R. J. Mathar_, Feb 03 2011
%e A100532 The fifth term is 2 + 3 + 5 + 7 = 17.
%t A100532 LinearRecurrence[{1,1,1,1}, {2,3,5,7}, 40] (* _G. C. Greubel_, Jun 30 2022 *)
%o A100532 (PARI) a(n)=([0,1,0,0; 0,0,1,0; 0,0,0,1; 1,1,1,1]^(n-1)*[2;3;5;7])[1,1] \\ _Charles R Greathouse IV_, Nov 01 2018
%o A100532 (Magma) [n le 4 select NthPrime(n) else Self(n-1)+Self(n-2)+Self(n-3)+Self(n-4): n in [1..41]]; // _G. C. Greubel_, Jun 30 2022
%o A100532 (SageMath)
%o A100532 @CachedFunction
%o A100532 def a(n): # a = A100532
%o A100532     if (n<5): return nth_prime(n)
%o A100532     else: return sum( a(n-j) for j in (1..4))
%o A100532 [a(n) for n in (1..40)] # _G. C. Greubel_, Jun 30 2022
%Y A100532 Cf. A000078, A001631.
%K A100532 easy,nonn
%O A100532 1,1
%A A100532 _Parthasarathy Nambi_, Nov 24 2004