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A214131 Partitions of n into parts congruent to +-4, +-6 (mod 13). 4
1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 8, 8, 10, 10, 12, 12, 15, 15, 18, 19, 22, 23, 27, 28, 32, 35, 39, 41, 47, 50, 56, 60, 67, 71, 80, 85, 94, 101, 113, 119, 132, 141, 156, 166, 183, 195, 215, 229, 250, 268, 293, 313, 341 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,13
COMMENTS
Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
LINKS
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of f(-x^13)^2 / (f(-x^4, -x^9) * f(-x^6, -x^7)) in powers of x where f() is Ramanujan's two-variable theta function.
Euler transform of period 13 sequence [ 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, ...].
G.f.: 1 / (Product_{k>0} (1 - x^(13*k - 4)) * (1 - x^(13*k - 6)) * (1 - x^(13*k - 7)) * (1 - x^(13*k - 9))).
A214129(n) = A214130(n) + a(n-1).
EXAMPLE
1 + x^4 + x^6 + x^7 + x^8 + x^9 + x^10 + x^11 + 2*x^12 + 2*x^13 + 2*x^14 + ...
q^5 + q^29 + q^41 + q^47 + q^53 + q^59 + q^65 + q^71 + 2*q^77 + 2*q^83 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ 1 / (QPochhammer[ q^4, q^13] QPochhammer[ q^6, q^13] QPochhammer[ q^7, q^13] QPochhammer[ q^9, q^13]), {q, 0, n}]
PROG
(PARI) {a(n) = if( n<0, 0, polcoeff( 1 / prod( k=1, n, 1 - [ 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0][k%13 + 1] * x^k, 1 + x * O(x^n)), n))}
CROSSREFS
Sequence in context: A053266 A112217 A172033 * A229977 A094994 A026839
KEYWORD
nonn
AUTHOR
Michael Somos, Jul 04 2012
STATUS
approved

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Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)