Search: id:A007531 Results 1-1 of 1 results found. %I A007531 M4159 %S A007531 0,0,0,6,24,60,120,210,336,504,720,990,1320,1716,2184,2730,3360,4080,4896, %T A007531 5814,6840,7980,9240,10626,12144,13800,15600,17550,19656,21924,24360, %U A007531 26970,29760,32736,35904,39270,42840,46620,50616,54834,59280,63960 %N A007531 n*(n-1)*(n-2) (or n!/(n-3)!). %C A007531 Ed Pegg Jr (ed(AT)mathpuzzle.com) conjectures that n^3 - n = k! has a solution iff n is 2, 3, 5 or 9 (when k is 3, 4, 5 and 6). %C A007531 Three-dimensional promic (or oblong) numbers, cf. A002378 - Alexandre Wajnberg (alexandre.wajnberg(AT)skynet.be), Dec 29 2005 %C A007531 Doubled first differences of tritriangular numbers A050534(n) = (1/8)n(n + 1)(n - 1)(n - 2). a(n) = 2*(A050534(n+1) - A050534(n)). - Alexander Adamchuk (alex(AT)kolmogorov.com), Apr 11 2006 %C A007531 If Y is a 4-subset of an n-set X then, for n>=6, a(n-4) is the number of (n-5)-subsets of X having exactly two elements in common with Y. - Milan R. Janjic (agnus(AT)blic.net), Dec 28 2007 %C A007531 Convolution of A005843 with A008585. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 07 2009] %C A007531 a(n) = A000578(n) - A000567(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 18 2009] %D A007531 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %D A007531 R. K. Guy, Unsolved Problems in Theory of Numbers, Section D25. %D A007531 L. B. W. Jolley, "Summation of Series", Dover Publications, 1961, p. 40. %H A007531 Index entries for two-way infinite sequences %H A007531 Index entries for sequences related to linear recurrences with constant coefficients %H A007531 Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets %F A007531 Sum(Polygorial(3, i), i=1..n) - Daniel Dockery (peritus(AT)gmail.com) Jun 16, 2003 %F A007531 a(0) = a(1) = a(2) = 0, a(n) = 3a(n-1) - 3a(n-2) + a(n-3) + 6. - Zak Seidov, (zakseidov(AT)yahoo.com) Feb 09 2006. %F A007531 G.f.: 6x^2/(1-x)^4. a(-n)=-a(n+2). %F A007531 1/6 + 3/24 + 5/60 +...= 3/4 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 21 2006 %F A007531 a(n)=numbperm(n,3). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2007 %F A007531 Other than the first two 0's this sequence is the same as the sequence a(n)=n^3-n. - Mohammad K. Azarian (azarian(AT)evansville.edu), Jul 26 2007 %F A007531 E.g.f.:x^3*exp(x) [From Geoffrey Critzer (critzer(AT)usd443.org), Feb 08 2009] %p A007531 [seq(6*binomial(n,3),n=0..41)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 24 2006 %p A007531 a:=n->sum(numbperm (n,2), j=0..n): seq(a(n), n=0..40); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 25 2007 %p A007531 seq(numbperm(n,3),n=0..41); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2007 %p A007531 a:=n->sum(sum(sum(1, j=0..n), k=1..n),m=2..n): seq(a(n), n=-1..40); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 18 2007 %p A007531 seq(sum(n^2-1, k=1..n), n=-1..39); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 28 2008 %p A007531 restart: G(x):=x^3*exp(x): f[0]:=G(x): for n from 1 to 41 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n],n=0..41);# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 05 2009] %t A007531 Table[n^3 - 3n^2 + 2n, {n, 0, 41}] %o A007531 (PARI) a(n)=n*(n-1)*(n-2) %Y A007531 Cf. A002378. %Y A007531 Equals 6*A000292(n-1). Cf. A002378, A005563, A084939, A084940, A084941, A084942, A084943, A084944. %Y A007531 Cf. A007531. %Y A007531 Sequence in context: A086768 A160944 A160936 this_sequence A130669 A101854 A101877 %Y A007531 Adjacent sequences: A007528 A007529 A007530 this_sequence A007532 A007533 A007534 %K A007531 nonn,easy %O A007531 0,4 %A A007531 N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com) Search completed in 0.002 seconds