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 A008384 Crystal ball sequence for A_4 lattice. 7
 1, 21, 131, 471, 1251, 2751, 5321, 9381, 15421, 24001, 35751, 51371, 71631, 97371, 129501, 169001, 216921, 274381, 342571, 422751, 516251, 624471, 748881, 891021, 1052501, 1235001, 1440271 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Partial sums of A008383. LINKS T. D. Noe, Table of n, a(n) for n = 0..1000 J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf). H. D. Nguyen, D. Taggart, Mining the OEIS: Ten Experimental Conjectures, 2013; Mentions this sequence. - From N. J. A. Sloane, Mar 16 2014 Index entries for crystal ball sequences Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA a(n) = 1 +5*n*(n+1)*(7*n^2+7*n+10)/12. - T. D. Noe, Apr 29 2007 G.f.: (-1-x^4-16*x^3-36*x^2-16*x)/(x-1)^5. [Maksym Voznyy (voznyy(AT)mail.ru), Aug 10 2009] a(n) = 5*a(n-1)-10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5), n> 4. - Harvey P. Dale, Aug 22 2011 MATHEMATICA Table[1/12 (12-50 n+85 n^2-70 n^3+35 n^4), {n, 30}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {1, 21, 131, 471, 1251}, 30] (* Harvey P. Dale, Aug 22 2011 *) PROG (PARI) a(n)=([0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; 1, -5, 10, -10, 5]^n*[1; 21; 131; 471; 1251])[1, 1] \\ Charles R Greathouse IV, Jun 15 2015 CROSSREFS Cf. A008383. Sequence in context: A219739 A228283 A157624 * A110400 A308348 A089369 Adjacent sequences: A008381 A008382 A008383 * A008385 A008386 A008387 KEYWORD nonn,nice,easy AUTHOR N. J. A. Sloane and J. H. Conway STATUS approved

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Last modified February 25 04:28 EST 2024. Contains 370309 sequences. (Running on oeis4.)