This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A111841 Number of partitions of 3^n-1 into powers of 3, also equals column 0 of triangle A111840, which shifts columns left and up under matrix cube. 3
 1, 1, 3, 18, 216, 5589, 336555, 49768101, 18707873562, 18299531019402, 47379925800261099, 328983441917303863134, 6190598463101580564238419, 318441251661562459898972204796, 45106336219710244780433937129788943 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Let q=3; a(n) equals the partitions of q^n-1 into powers of q, or, the coefficient of x^(q^n-1) in 1/Product_{j>=0}(1-x^(q^j)). LINKS T. D. Noe, Table of n, a(n) for n=0..40 FORMULA a(n) = [x^(3^n-1)] Product_{k>=0} 1/(1-x^(3^k)). PROG (PARI) {a(n, q=3)=local(A=Mat(1), B); if(n<0, 0, for(m=1, n+1, B=matrix(m, m); for(i=1, m, for(j=1, i, if(j==i, B[i, j]=1, if(j==1, B[i, j]=(A^q)[i-1, 1], B[i, j]=(A^q)[i-1, j-1])); )); A=B); return(A[n+1, 1]))} CROSSREFS Cf. A111840, A078124 (variant). Cf. A002449. Sequence in context: A163883 A319580 A132727 * A279233 A071605 A222686 Adjacent sequences:  A111838 A111839 A111840 * A111842 A111843 A111844 KEYWORD nonn AUTHOR Paul D. Hanna, Aug 22 2005 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 14 17:41 EST 2019. Contains 329979 sequences. (Running on oeis4.)