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.

2, 3, 5, 7, 17, 32, 61, 117, 227, 437, 842, 1623, 3129, 6031, 11625, 22408, 43193, 83257, 160483, 309341, 596274, 1149355, 2215453, 4270423, 8231505, 15866736, 30584117, 58952781, 113635139, 219038773, 422210810, 813837503, 1568722225, 3023809311, 5828579849

Offset

1,1

Links

Table of n, a(n) for n=1..35.

Martin Burtscher, Igor Szczyrba, and Rafał Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.

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

Formula

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.

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

Example

The fifth term is 2 + 3 + 5 + 7 = 17.

Mathematica

LinearRecurrence[{1, 1, 1, 1}, {2, 3, 5, 7}, 40] (* G. C. Greubel, Jun 30 2022 *)

Prog

(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
(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
(SageMath)
@CachedFunction
def a(n): # a = A100532
    if (n<5): return nth_prime(n)
    else: return sum( a(n-j) for j in (1..4))
[a(n) for n in (1..40)] # G. C. Greubel, Jun 30 2022

Crossrefs

Cf. A000078, A001631.

Sequence in context: A143027 A001153 A141453 * A231480 A040149 A168034

Adjacent sequences: A100529 A100530 A100531 * A100533 A100534 A100535

Keyword

easy,nonn

Author

Parthasarathy Nambi, Nov 24 2004

Status

approved