The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A208856 Partitions of n into parts not congruent to 0, +-4, +-6, +-10, 16 (mod 32). 3
 1, 1, 2, 3, 4, 6, 8, 11, 15, 20, 26, 34, 44, 56, 72, 91, 114, 143, 178, 220, 272, 334, 408, 498, 605, 732, 884, 1064, 1276, 1528, 1824, 2171, 2580, 3058, 3616, 4269, 5028, 5910, 6936, 8124, 9498, 11088, 12922, 15034, 17468, 20264, 23472, 27154, 31369, 36189 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700). Andrews (1987) refers to this sequence as p(T, n) where T is the set in equation (1) on page 437. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 G. E. Andrews, Unsolved Problems: Further Problems on Partitions, Amer. Math. Monthly 94 (1987), no. 5, 437-439. Michael Somos, Introduction to Ramanujan theta functions Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of (f(x) / f(-x) - 1) / (2 * x) in powers of x where f() is a Ramanujan theta function. Expansion of (f(x^14, x^34) - x^4 * f(x^2, x^46)) / f(-x, -x^2) in powers of x where f() is Ramanujan's two-variable theta function. Euler transform of period 32 sequence [ 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, ...]. a(n) = A115671(n + 1). 2 * a(n) = A080054(n + 1). a(2*n) = A187154(n). a(2*n + 1) = A208851(n). EXAMPLE 1 + x + 2*x^2 + 3*x^3 + 4*x^4 + 6*x^5 + 8*x^6 + 11*x^7 + 15*x^8 + 20*x^9 + ... a(5) = 6 since 5 = 3 + 2 = 3 + 1 + 1 = 2 + 2 + 1 = 2 + 1 + 1 + 1 = 1 + 1 + 1 + 1 + 1 in 6 ways. a(6) = 8 since 5 + 1 = 3 + 3 = 3 + 2 + 1 = 3 + 1 + 1 + 1 = 2 + 2 + 2 = 2 + 2 + 1 + 1 = 2 + 1 + 1 + 1 + 1 = 1 + 1 + 1 + 1 + 1 + 1 in 8 ways. MATHEMATICA A208856[n_] := SeriesCoefficient[(1/(2*q))*((QPochhammer[-q, -q]/ QPochhammer[q, q]) - 1), {q, 0, n}]; Table[A208856[n], {n, 0, 50}] (* G. C. Greubel, Jun 19 2017 *) PROG (PARI) {a(n) = local(A); if( n<0, 0, n++; A = x * O(x^n); polcoeff( (eta(x^2 + A)^3 / (eta(x + A)^2 * eta(x^4 + A)) - 1) / 2, n))} CROSSREFS Cf. A080054, A115671, A187154, A208851. Sequence in context: A224216 A245432 A115671 * A105782 A035956 A035963 Adjacent sequences: A208853 A208854 A208855 * A208857 A208858 A208859 KEYWORD nonn AUTHOR Michael Somos, Mar 02 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 5 05:01 EST 2023. Contains 367575 sequences. (Running on oeis4.)