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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. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

Martin Burtscher, Igor Szczyrba, and RafaƂ 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

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Last modified October 5 14:56 EDT 2022. Contains 357259 sequences. (Running on oeis4.)