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 A118061 9800*n^2-5740*n-4059 5
 1, 23661, 66921, 129781, 212241, 314301, 435961, 577221, 738081, 918541, 1118601, 1338261, 1577521, 1836381, 2114841, 2412901, 2730561, 3067821, 3424681, 3801141, 4197201, 4612861, 5048121, 5502981, 5977441, 6471501 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS In general, all sequences of equations which contain every positive integer in order exactly once (a pairwise equal summed, ordered partition of the positive integers) may be defined as follows: For all k, let x(k)=A001652(k) and z(k)=A001653(k). Then if we define a(n) to be (x(k)+z(k))n^2-(z(k)-1)n-x(k), the following equation is true: a(n)+(a(n)+1)+...+(a(n)+(x(k)+z(k))n+(2x(k)+z(k)-1)/2)=(a(n)+ (x(k)+z(k))n+(2x(k)+z(k)+1)/2)+...+(a(n)+2(x(k)+z(k))n+x(k)); a(n)+2(x(k)+z(k))n+x(k))=a(n+1)-1; e.g., in this sequence, x(5)=A001652(5)=4059 and z(5)=A001653(5)=5741; cf. A000290,A118057-A118060. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n)+(a(n)+1)+...+(a(n)+9800n+6929)=(a(n)+9800n+6930)+...+(a(n)+19600n+4059); a(n)+19600n+4059=a(n+1)-1; a(n+1)-1=a(n)+19600n+4059. a(n)+(a(n)+1)+...+(a(n)+576n+203)=35(140n-41)(140n+29)(140n+99); e.g., 66921+66922+...+103250=3091156215=35*379*449*519. a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). G.f.: x*(1+23658*x-4059*x^2)/(1-x)^3. - Colin Barker, Jul 01 2012 EXAMPLE a(3)= 9800*3^2-5740*3-4059=66921, a(4)=9800*4^2-5740*4-4059=129781 and 66921+66922+...+103250=103251+...+129780 MATHEMATICA CoefficientList[Series[(1+23658*x-4059*x^2)/(1-x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Jul 09 2012 *) PROG (MAGMA) [9800*n^2-5740*n-4059: n in [1..40]]; // Vincenzo Librandi, Jul 09 2012 (PARI) a(n)=9800*n^2-5740*n-4059 \\ Charles R Greathouse IV, May 10 2016 CROSSREFS Sequence in context: A304652 A230361 A069334 * A251855 A200437 A223342 Adjacent sequences:  A118058 A118059 A118060 * A118062 A118063 A118064 KEYWORD nonn,easy,less AUTHOR Charlie Marion, Apr 26 2006 EXTENSIONS Corrected by T. D. Noe, Nov 13 2006 STATUS approved

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Last modified December 11 21:28 EST 2018. Contains 318052 sequences. (Running on oeis4.)