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A157101 A Somos-4 variant. 4
1, -1, -5, -4, 29, 129, -65, -3689, -16264, 113689, 2382785, 7001471, -398035821, -7911171596, 43244638645, 6480598259201, 124106986093951, -5987117709349201, -541051130050800400, -4830209396684261199 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Hankel transform of A157100.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..145

Paul Barry, Generalized Catalan recurrences, Riordan arrays, elliptic curves, and orthogonal polynomials, arXiv:1910.00875 [math.CO], 2019.

FORMULA

a(n) = (a(n-1)*a(n-3) + a(n-2)^2)/a(n-4), with a(0)=1, a(1)=-1, a(2)=-5, a(3)=-4.

a(n) = A051138(n+1) for all n in Z. - Michael Somos, Jul 17 2016

MATHEMATICA

RecurrenceTable[{a[n]==(a[n-1]*a[n-3]+a[n-2]^2)/a[n-4], a[0]==1, a[1]==-1, a[2]==-5, a[3]==-4}, a, {n, 20}] (* G. C. Greubel, Feb 23 2019 *)

PROG

(PARI) m=20; v=concat([1, -1, -5, -4], vector(m-4)); for(n=5, m, v[n] = (v[n-1]*v[n-3] +v[n-2]^2)/v[n-4]); v \\ G. C. Greubel, Feb 23 2019

(MAGMA) I:=[1, -1, -5, -4]; [n le 4 select I[n] else (Self(n-1)*Self(n-3) + Self(n-2)^2)/Self(n-4): n in [1..20]]; // G. C. Greubel, Feb 23 2019

(Sage)

def a(n):

    if (n==0): return 1

    elif (n==1): return -1

    elif (n==2): return -5

    elif (n==3): return -4

    else: return (a(n-1)*a(n-3) + a(n-2)^2)/a(n-4)

[a(n) for n in (0..20)] # G. C. Greubel, Feb 23 2019

(GAP) a:=[1, -1, -5, -4];; for n in [5..20] do a[n]:=(a[n-1]*a[n-3] + a[n-2]^2)/a[n-4]; od; a; # G. C. Greubel, Feb 23 2019

CROSSREFS

Cf. A051138.

Cf. A157005, A162546, A162547.

Sequence in context: A024067 A192778 A051138 * A237648 A091001 A297936

Adjacent sequences:  A157098 A157099 A157100 * A157102 A157103 A157104

KEYWORD

easy,sign

AUTHOR

Paul Barry, Feb 22 2009

STATUS

approved

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Last modified May 13 14:47 EDT 2021. Contains 343860 sequences. (Running on oeis4.)