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 A177342 a(n) = (4*n^3-3*n^2+5*n-3)/3. 9
 1, 9, 31, 75, 149, 261, 419, 631, 905, 1249, 1671, 2179, 2781, 3485, 4299, 5231, 6289, 7481, 8815, 10299, 11941, 13749, 15731, 17895, 20249, 22801, 25559, 28531, 31725, 35149, 38811, 42719, 46881, 51305, 55999, 60971, 66229, 71781, 77635 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This sequence is related to the fourth powers (A000583) by n^4 = n*a(n) - Sum_{i=1..n-1} a(i) - (n-1), with n>1. Also, n*a(n) - Sum_{i=1..n-1} a(i) provides the first column of A162624 and the second column of A162622 (or A162623). - Bruno Berselli, revised Dec 14 2012 LINKS B. Berselli, Table of n, a(n) for n = 1..10000 Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA G.f.: x*(1 + 5*x + x^2 + x^3)/(1 - x)^4. a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). a(n) - a(-n) = 2*A004006(2n). a(n) + a(-n) = -A002522(n). a(n) = 1 + (n-1)*(4*n^2+n+6)/3 = 2*A174723(n)-1. MATHEMATICA CoefficientList[Series[(1 + 5 x + x^2 + x^3) / (1 - x)^4, {x, 0, 50}], x] (* Vincenzo Librandi, Aug 19 2013 *) Table[(4 n^3 - 3 n^2 + 5 n - 3)/3, {n, 1, 40}] (* Bruno Berselli, Feb 17 2015 *) PROG (PARI) a(n)=(4*n^3-3*n^2+5*n-3)/3 \\ Charles R Greathouse IV, Jun 23 2011 (MAGMA) [(4*n^3-3*n^2+5*n-3)/3: n in [1..39]]; // Bruno Berselli, Aug 24 2011 (MAGMA) I:=[1, 9, 31, 75]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Aug 19 2013 CROSSREFS First differences: 2*A084849. Partial sums: A178073. Cf. A174723, A162622-A162624. Sequence in context: A288419 A168297 A004126 * A224000 A118444 A321598 Adjacent sequences:  A177339 A177340 A177341 * A177343 A177344 A177345 KEYWORD nonn,easy AUTHOR Bruno Berselli, May 06 2010 - Nov 27 2010 EXTENSIONS Formulae added and revised by Bruno Berselli, Feb 17 2015 STATUS approved

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Last modified September 18 12:00 EDT 2019. Contains 327170 sequences. (Running on oeis4.)