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

Author

Parthasarathy Nambi, Nov 24 2004

Keywords

• easy
• nonn

Examples

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

Links

• 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).

Crossrefs

Cf. A000078, A001631.

Programs

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

Mathematica

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

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

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

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