The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A280457 Expansion of Product_{k>=0} (1 + x^(7*k+1)). 14
 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 1, 3, 2, 0, 0, 0, 0, 1, 3, 3, 1, 0, 0, 0, 1, 4, 4, 1, 0, 0, 0, 1, 4, 5, 2, 0, 0, 0, 1, 5, 7, 3, 0, 0, 0, 1, 5, 8, 5, 1, 0, 0, 1, 6, 10, 6, 1, 0, 0, 1, 6, 12, 9, 2, 0, 0, 1, 7, 14, 11, 3, 0, 0, 1, 7, 16, 15, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,24 COMMENTS Number of partitions of n into distinct parts congruent to 1 mod 7. LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 Vaclav Kotesovec, A method of finding the asymptotics of q-series based on the convolution of generating functions, arXiv:1509.08708 [math.CO], Sep 30 2015. FORMULA G.f.: Product_{k>=0} (1 + x^(7*k+1)). a(n) ~ exp(Pi*sqrt(n)/sqrt(21))/(2*2^(1/7)*21^(1/4)*n^(3/4)) * (1 + (13*Pi/(336*sqrt(21)) - 3*sqrt(21)/(8*Pi)) / sqrt(n)). - Ilya Gutkovskiy, Jan 03 2017, extended by Vaclav Kotesovec, Jan 24 2017 EXAMPLE a(37) = 3 because we have [36, 1], [29, 8] and [22, 15]. MATHEMATICA nmax = 105; CoefficientList[Series[Product[(1 + x^(7 k + 1)), {k, 0, nmax}], {x, 0, nmax}], x] nmax = 200; poly = ConstantArray[0, nmax + 1]; poly[[1]] = 1; poly[[2]] = 1; Do[If[Mod[k, 7] == 1, Do[poly[[j + 1]] += poly[[j - k + 1]], {j, nmax, k, -1}]; ], {k, 2, nmax}]; poly (* Vaclav Kotesovec, Jan 18 2017 *) CROSSREFS Cf. A000700, A016993, A169975, A261612, A280454. Cf. A262928, A147599, A281243, A281244. Cf. A109703, A281245, A281455, A281456, A281457, A281458, A281459. Sequence in context: A284504 A281245 A284499 * A308118 A017857 A127842 Adjacent sequences:  A280454 A280455 A280456 * A280458 A280459 A280460 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Jan 03 2017 STATUS approved

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

Last modified September 27 10:28 EDT 2021. Contains 347689 sequences. (Running on oeis4.)