The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons 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 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A035147 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s) + Kronecker(m,p)*p^(-2s))^(-1) for m = -43. 7
 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 1, 2, 0, 0, 2, 0, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,11 COMMENTS From Jianing Song, Sep 07 2018: (Start) Half of the number of integer solutions to x^2 + x*y + 11*y^2 = n. Inverse Moebius transform of A011591. (End) LINKS G. C. Greubel, Table of n, a(n) for n = 1..10000 FORMULA From Jianing Song, Sep 07 2018: (Start) a(n) is multiplicative with a(43^e) = 1, a(p^e) = (1 + (-1)^e) / 2 if Kronecker(-43, p) = -1, a(p^e) = e + 1 if Kronecker(-43, p) = 1. G.f.: Sum_{k>0} Kronecker(-43, k) * x^k / (1 - x^k). A138811(n) = 2 * a(n) unless n = 0. (End) MATHEMATICA a[n_] := If[n < 0, 0, DivisorSum[n, KroneckerSymbol[-43, #] &]]; Table[a[n], {n, 1, 100}] (* G. C. Greubel, Apr 25 2018 *) PROG (PARI) m=-43; direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X)) CROSSREFS Cf. A138811. Moebius transform gives A011591. Sequence in context: A030219 A287345 A260675 * A101673 A091395 A248107 Adjacent sequences:  A035144 A035145 A035146 * A035148 A035149 A035150 KEYWORD nonn,mult AUTHOR 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 December 7 07:57 EST 2021. Contains 349571 sequences. (Running on oeis4.)