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A003303 Numerators of spin-wave coefficients for cubic lattice.
(Formerly M4672)
1
1, 9, 297, 7587, 1086939, 51064263, 5995159677, 423959714955, 281014370213715, 26702465299878195, 5723872792950096855, 682922353396120790085, 358992734790795421416975, 51516147618272668808063475 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

G. S. Joyce, The simple cubic lattice Green function, Phil. Trans. Roy. Soc., 273 (1972), 583-610.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 18 2008, Table of n, a(n) for n = 0..20

FORMULA

Let g(n) be the sequence of rational numbers defined by the recurrence: 256(n+1)g(n+1)-32(22n^2+22n+9)g(n)+144n(4n^2+1)g(n-1)-9(2n-1)^4g(n-2)=0 (n>=0) with g(-2)=g(-1)=0 and g(1)=1. Then a(n) is the numerator of g(n) - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 18 2008

PROG

(PARI) g=vector(100); g[3]=1; print1("1, "); for(n=1, 30, g[n+3]=(32*(22*(n^2-n)+9)*g[n+2]-144*(n-1)*(4*(n-1)^2+1)*g[n+1]+9*(2*n-3)^4*g[n])/(256*n); print1(numerator(g[n+3])", ")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 18 2008

CROSSREFS

Sequence in context: A027834 A175823 A129934 * A012838 A216966 A211077

Adjacent sequences:  A003300 A003301 A003302 * A003304 A003305 A003306

KEYWORD

nonn,easy,frac

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 18 2008

STATUS

approved

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Last modified January 21 19:51 EST 2019. Contains 319350 sequences. (Running on oeis4.)