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Demonstration of theOnLine Encyclopedia of Integer Sequences® (OEIS®)(Page 11)
Superseeker
The following is an essentially unedited copy of Superseeker's reply to a recent submission from a crystallographer in Switzerland. The received message said:
lookup 1 10 36 91 190 351 The following is Superseeker's response.
Report on [ 1,10,36,91,190,351]: Many tests are carried out, but only potentially useful information (if any) is reported here. TEST: IS THE NTH TERM A POLYNOMIAL IN N? SUCCESS: nth term is nontrivial polynomial in n of degree 4 Polynomial is: 1+15/4*n+31/8*n^2+5/4*n^3+1/8*n^4 Even though there are a large number of sequences in the OEIS, at least one of yours is not there! If it is of general interest, please submit it using the submission form http://oeis.org/Submit.html and it will (probably) be added! Thanks! TRY "RATE", CHRISTIAN KRATTHENTALER'S MATHEMATICA PROGRAM FOR GUESSING A CLOSED FORM FOR A SEQUENCE. ("Rate" is "Guess" in German. For a description of RATE, see http://radon.mat.univie.ac.at/People/kratt/rate/rate.html) RATE found the following formula for the nth term: Warning: as with all these guessing programs, this is only a suggestion! (n*(3 + n)*(2 + 3*n + n^2))/8 TEST: APPLY VARIOUS TRANSFORMATIONS TO SEQUENCE AND LOOK IT UP IN THE ENCYCLOPEDIA AGAIN SUCCESS (limited to 40 matches): Transformation T050 gave a match with: %I A021247 %S A021247 0,0,4,1,1,5,2,2,6,3,3,7,4,4,8,5,5,9,6,7,0,7,8,1,8,9,3,0,0,4,1,1,5, %T A021247 2,2,6,3,3,7,4,4,8,5,5,9,6,7,0,7,8,1,8,9,3,0,0,4,1,1,5,2,2,6,3,3,7, %U A021247 4,4,8,5,5,9,6,7,0,7,8,1,8,9,3,0,0,4,1,1,5,2,2,6,3,3,7,4,4,8,5,5,9 %N A021247 Decimal expansion of 1/243. %K A021247 nonn,cons %O A021247 0,3 %A A021247 N. J. A. Sloane (njas(AT)research.att.com) Transformation T019 gave a match with: %I A009879 %S A009879 1,4,9,17,29,44,62,85,112,139,169,206,247,292,336,380,434,492,548,607, %T A009879 676,755,832,904,982,1067,1156,1247,1340,1444,1554,1661,1765,1865, %U A009879 1973,2098,2228,2358,2488,2621,2765,2905,3032,3165,3316,3478,3642,3806 %N A009879 Coordination sequence T5 for Zeolite Code DFO. %D A009879 R. W. GrosseKunstleve, G. O. Brunner and N. J. A. Sloane, Algebraic Description of Coordination Sequences and Exact Topological Densities for Zeolites, Acta Cryst., A52 (1996), pp. 879889. %D A009879 W.M. Meier, D.H. Olson and Ch. Baerlocher, Atlas of Zeolite Structure Types, 4th Ed., Elsevier, 1996 %H A009879 GrosseKunstleve et al. paper %H A009879 Coordination Sequences and Encyclopedia of Integer Sequences %K A009879 nonn %O A009879 0,2 %A A009879 rwgk(AT)cci.lbl.gov (R.W. GrosseKunstleve) List of transformations used: T019 sequence u[j+2]2*u[j+1]+u[j] T050 jth coefficient of Sn(z)*(1z)^j Abbreviations used in the above list of transformations: u[j] = jth term of the sequence v[j] = u[j]/(j1)! Sn(z) = ordinary generating function En(z) = exponential generating function Comments
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