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

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A323016 a(n) is the number of ordered partitions of 24*n + 4 into four squares of primes (A001248). 1
 0, 0, 0, 0, 1, 4, 6, 4, 5, 12, 16, 16, 18, 16, 18, 28, 34, 28, 26, 36, 49, 40, 44, 52, 42, 52, 70, 52, 47, 60, 76, 72, 54, 76, 60, 48, 88, 68, 50, 72, 78, 80, 48, 96, 102, 60, 98, 76, 79, 96, 104, 112, 52, 108, 132, 64, 112, 88, 94, 120, 89, 136, 72, 88, 168, 96 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS The main entry is A323015, which is the unordered version. Also, a(n) is the number of ordered partitions of n into four terms of A024702. a(n) > 0 for 4 <= n <= 2*10^4. Conjecture: a(n) > 0 for all n >= 4. A stronger conjecture: lim inf a(n) = +oo. LINKS FORMULA G.f.: (Sum_{primes p>=5} x^((p^2-1)/24))^4 = (Sum_{k>=3} x^A024702(k))^4. EXAMPLE 100 = 5^2 + 5^2 + 5^2 + 5^2 (1 permutation). 124 = 5^2 + 5^2 + 5^2 + 7^2 (4 permutations). 148 = 5^2 + 5^2 + 7^2 + 7^2 (6 permutations). 172 = 5^2 + 7^2 + 7^2 + 7^2 (4 permutations). 196 = 7^2 + 7^2 + 7^2 + 7^2 (1 permutation) = 5^2 + 5^2 + 5^2 + 11^2 (4 permutations). 220 = 5^2 + 5^2 + 7^2 + 11^2 (12 permutations). 244 = 5^2 + 7^2 + 7^2 + 11^2 (12 permutations) = 5^2 + 5^2 + 5^2 + 13^2 (4 permutations). 268 = 7^2 + 7^2 + 7^2 + 11^2 (4 permutations) = 5^2 + 5^2 + 7^2 + 13^2 (12 permutations). ... PROG (PARI) a(n) = if(n<4, 0, polcoeff(sum(p=5, sqrt(24*n-48), if(isprime(p), x^((p^2-1)/24), 0))^4, n)) CROSSREFS Cf. A001248, A024702, A323015. Sequence in context: A123999 A014110 A266491 * A261637 A091651 A199865 Adjacent sequences:  A323013 A323014 A323015 * A323017 A323018 A323019 KEYWORD nonn AUTHOR Jianing Song, Jan 05 2019 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 January 19 18:25 EST 2020. Contains 331051 sequences. (Running on oeis4.)