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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A219331 L.g.f.: -log(1 - Sum_{n>=1} x^(n^2))  =  Sum_{n>=1} a(n)*x^n/n. 4
 1, 1, 1, 5, 6, 7, 8, 13, 28, 36, 45, 59, 92, 134, 186, 269, 375, 538, 761, 1080, 1520, 2157, 3060, 4339, 6181, 8750, 12394, 17554, 24912, 35322, 50066, 70957, 100596, 142665, 202278, 286790, 406520, 576347, 817142, 1158528, 1642461, 2328536, 3301283, 4680417, 6635688 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Limit a(n)/a(n+1) = 0.705346681379806989636379706393941505260078161512292870... is a real root of 1 = Sum_{n>=1} x^(n^2). LINKS Paul D. Hanna, Table of n, a(n) for n = 1..1000 FORMULA Logarithmic derivative of A006456, where A006456(n) is the number of compositions of n into sums of squares. EXAMPLE L.g.f.: L(x) = x + x^2/2 + x^3/3 + 5*x^4/4 + 6*x^5/5 + 7*x^6/6 + 8*x^7/7 + 13*x^8/8 + 28*x^9/9 + 36*x^10/10 +... where exp(L(x)) = 1 + x + x^2 + x^3 + 2*x^4 + 3*x^5 + 4*x^6 + 5*x^7 + 7*x^8 + 11*x^9 + 16*x^10 + 22*x^11 + 30*x^12 +...+ A006456(n)*x^n +... exp(-L(x)) = 1 - x - x^4 - x^9 - x^16 - x^25 - x^36 +...+ -x^(n^2) +... PROG (PARI) {a(n)=n*polcoeff(-log(1-sum(r=1, sqrtint(n+1), x^(r^2)+x*O(x^n))), n)} for(n=1, 50, print1(a(n), ", ")) CROSSREFS Cf. A224607, A224608, A006456. Sequence in context: A171405 A047575 A014097 * A229862 A302599 A098670 Adjacent sequences:  A219328 A219329 A219330 * A219332 A219333 A219334 KEYWORD nonn AUTHOR Paul D. Hanna, Apr 12 2013 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 June 28 17:31 EDT 2022. Contains 354907 sequences. (Running on oeis4.)