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A072684 Expansion of (2+x+3*x^2+2*x^3+x^4)/(1-x-5*x^2+x^3+3*x^4-x^5). 0
2, 3, 16, 31, 103, 235, 674, 1669, 4526, 11595, 30769, 79885, 210226, 548623, 1439156, 3763159, 9859523, 25800519, 67566130, 176858881, 463073602, 1212259843, 3173871101, 8309086201, 21753819938, 56951673915, 149102333944 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

S. Ramanujan, Note on a set of Simultaneous Equations, J. Indian Math. Soc., 4(1912), 94-96.

LINKS

Table of n, a(n) for n=0..26.

Index entries for linear recurrences with constant coefficients, signature (1, 5, -1, -3, 1).

FORMULA

G.f.: (2+x+3*x^2+2*x^3+x^4)/(1-x-5*x^2+x^3+3*x^4-x^5).

a(n)=2*a(n-1)+3*a(n-2)-4*a(n-3)+a(n-4)+3*(-1)^n.

EXAMPLE

2 + 3*x + 16*x^2 + 31*x^3 + 103*x^4 + 235*x^5 + 674*x^6 + 1669*x^7 + 4526*x^8 + ...

MATHEMATICA

CoefficientList[Series[(2+x+3x^2+2x^3+x^4)/(1-x-5x^2+x^3+3x^4-x^5), {x, 0, 40}], x] (* or *) LinearRecurrence[{1, 5, -1, -3, 1}, {2, 3, 16, 31, 103}, 40] (* Harvey P. Dale, Sep 23 2018 *)

PROG

(PARI) {a(n) = if( n<0, 0, polcoeff( (2 + x + 3*x^2 + 2*x^3 + x^4) / (1 - x - 5*x^2 + x^3 + 3*x^4 - x^5) + x * O(x^n), n))}

CROSSREFS

Sequence in context: A034382 A034383 A350025 * A344747 A073633 A012357

Adjacent sequences:  A072681 A072682 A072683 * A072685 A072686 A072687

KEYWORD

nonn,easy

AUTHOR

Michael Somos, Jul 01 2002

STATUS

approved

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Last modified January 27 15:42 EST 2022. Contains 350607 sequences. (Running on oeis4.)