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 A010008 a(0) = 1, a(n) = 18*n^2 + 2 for n>0. 3
 1, 20, 74, 164, 290, 452, 650, 884, 1154, 1460, 1802, 2180, 2594, 3044, 3530, 4052, 4610, 5204, 5834, 6500, 7202, 7940, 8714, 9524, 10370, 11252, 12170, 13124, 14114, 15140, 16202, 17300, 18434, 19604, 20810, 22052, 23330, 24644, 25994, 27380, 28802, 30260 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The identity (18*n^2+2)^2-(9*n^2+2)*(6*n)^2=4 can be written as a(n+1)^2-A010002(n+1)*A008588(n+1)^2=4. - Vincenzo Librandi, Feb 07 2012 LINKS Bruno Berselli, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA G.f.: (1+x)*(1+16*x+x^2)/(1-x)^3. - Bruno Berselli, Feb 06 2012 a(n) = (3*n-1)^2+(3*n+1)^2 = (n-1)^2+(n+1)^2+(4*n)^2 for n>0. - Bruno Berselli, Feb 06 2012 E.g.f.: (x*(x+1)*18+2)*e^x-1. - Gopinath A. R., Feb 14 2012 MATHEMATICA Join[{1}, 18 Range[41]^2 + 2] (* Bruno Berselli, Feb 06 2012 *) Join[{1}, LinearRecurrence[{3, -3, 1}, {20, 74, 164}, 50]] (* Vincenzo Librandi, Aug 03 2015 *) PROG (Magma) [1] cat [18*n^2+2: n in [1..50]]; // Vincenzo Librandi, Aug 03 2015 CROSSREFS After 20, all terms are in A000408. Cf. A206399. Sequence in context: A002292 A225923 A238026 * A237617 A000529 A238027 Adjacent sequences: A010005 A010006 A010007 * A010009 A010010 A010011 KEYWORD nonn,easy AUTHOR N. J. A. Sloane. EXTENSIONS More terms from Bruno Berselli, Feb 06 2012 STATUS approved

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Last modified September 29 14:55 EDT 2023. Contains 365772 sequences. (Running on oeis4.)