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 A261343 50-gonal numbers: a(n) = 48*n*(n-1)/2 + n. 1
 0, 1, 50, 147, 292, 485, 726, 1015, 1352, 1737, 2170, 2651, 3180, 3757, 4382, 5055, 5776, 6545, 7362, 8227, 9140, 10101, 11110, 12167, 13272, 14425, 15626, 16875, 18172, 19517, 20910, 22351, 23840, 25377, 26962, 28595, 30276, 32005, 33782, 35607, 37480 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS According to the common formula for the polygonal numbers: (s-2)*n*(n-1)/2 + n (here s = 50). 96*a(n) + 23^2 is a square. LINKS Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = n*(24*n - 23). G.f.: x*(1+47*x)/(1-x)^3. - Vincenzo Librandi, Aug 17 2015 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Aug 17 2015 MAPLE A261343:=n->n*(24*n-23): seq(A261343(n), n=0..40); # Wesley Ivan Hurt, Aug 20 2015 PROG (JavaScript) function a(n){return 48*n*(n-1)/2+n} (PARI) first(m)=vector(m, n, n--; n*(24*n-23)) \\ Anders HellstrÃ¶m, Aug 15 2015 (MAGMA) [n*(24*n-23): n in [0..40]]; // Vincenzo Librandi, Aug 17 2015 CROSSREFS Cf. A001107, A051872, A254474. Sequence in context: A235942 A093300 A283392 * A104152 A044382 A044763 Adjacent sequences:  A261340 A261341 A261342 * A261344 A261345 A261346 KEYWORD nonn,easy AUTHOR Sergey Pavlov, Aug 15 2015 STATUS approved

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