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 A093916 a(2*k-1)=(2*k-1)^2+2-k, a(2*k)=6*k^2+2-k: First column of the triangle A093915. 4
 2, 7, 9, 24, 24, 53, 47, 94, 78, 147, 117, 212, 164, 289, 219, 378, 282, 479, 353, 592, 432, 717, 519, 854, 614, 1003, 717, 1164, 828, 1337, 947, 1522, 1074, 1719, 1209, 1928, 1352, 2149, 1503, 2382, 1662, 2627, 1829, 2884, 2004, 3153, 2187, 3434, 2378, 3727, 2577, 4032, 2784, 4349, 2999, 4678, 3222, 5019, 3453, 5372, 3692, 5737, 3939, 6114, 4194, 6503, 4457, 6904, 4728, 7317, 5007, 7742, 5294, 8179, 5589, 8628, 5892, 9089 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The sequence was initially defined as the first column of the triangle A093915, constructed by trial and error. It is however easy to prove that the sum of the r-th row of A093915, A093917(r), equals twice A006003(r) when r is odd, and three times A006003(r) when r is even. Given the expression of the row sum A093917(r) in terms of the first element a(r), one obtains the explicit formula for a(r). - M. F. Hasler, Apr 04 2009 LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1). FORMULA a(n) = ((n^2+1)*b(n)-n+1)/2 where b(n) = 3-(n%2) = 2 if n odd, = 3 if n even. - M. F. Hasler, Apr 04 2009 a(n) = (n*(5*n-2)+(n^2+1)*(-1)^n+7)/4. a(n) = 3*a(n-2)-3*a(n-4)+a(n-6). G.f.: x*(2+7*x+3*x^2+3*x^3+3*x^4+2*x^5)/((1-x)^3*(1+x)^3). - Colin Barker, May 01 2012 MATHEMATICA LinearRecurrence[{0, 3, 0, -3, 0, 1}, {2, 7, 9, 24, 24, 53}, 80] (* Harvey P. Dale, Nov 24 2017 *) PROG (PARI code by M. F. Hasler, Apr 04 2009) A093916(n)=((n^2+1)*(3-n%2)-n+1)/2 /* or the "experimental" version, trying out all allowed values */ A093916(n)={ local( s=(n^3+n)/2, d=(n^2-n)/2, k=ceil((2*s-d)/n)); while( (n*k+d)%s, k++ ); k } CROSSREFS Cf. A093915, A093917, A093918. Sequence in context: A321322 A343495 A065139 * A042451 A042929 A082962 Adjacent sequences:  A093913 A093914 A093915 * A093917 A093918 A093919 KEYWORD nonn,easy AUTHOR Amarnath Murthy, Apr 25 2004 EXTENSIONS Edited and extended by M. F. Hasler, Apr 04 2009 STATUS approved

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Last modified May 6 00:41 EDT 2021. Contains 343579 sequences. (Running on oeis4.)