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 A226450 a(n) = n*(3*n^2 - 5*n + 3). 3
 0, 1, 10, 45, 124, 265, 486, 805, 1240, 1809, 2530, 3421, 4500, 5785, 7294, 9045, 11056, 13345, 15930, 18829, 22060, 25641, 29590, 33925, 38664, 43825, 49426, 55485, 62020, 69049, 76590, 84661, 93280, 102465, 112234, 122605, 133596, 145225, 157510, 170469 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS See the comment in A226449. For n >= 3, also the detour index of the n-barbell graph. - Eric W. Weisstein, Dec 20 2017 LINKS Bruno Berselli, Table of n, a(n) for n = 0..1000 Eric Weisstein's World of Mathematics, Barbell Graph Eric Weisstein's World of Mathematics, Detour Index Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA G.f.: x*(1+6*x+11*x^2)/(1-x)^4. a(n) = A000567(n) + n*A000567(n-1). MATHEMATICA Table[n (3 n^2 - 5 n + 3), {n, 0, 40}] CoefficientList[Series[x (1 + 6 x + 11 x^2)/(1 - x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Aug 18 2013 *) LinearRecurrence[{4, -6, 4, -1}, {1, 10, 45, 124}, {0, 20}] (* Eric W. Weisstein, Dec 20 2017 *) PROG (MAGMA) [n*(3*n^2-5*n+3): n in [0..40]]; (MAGMA) I:=[0, 1, 10, 45]; [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..45]]; // Vincenzo Librandi, Aug 18 2013 (PARI) a(n) = n*(3*n^2 - 5*n + 3); \\ Altug Alkan, Dec 20 2017 CROSSREFS Cf. A000567. Similar sequences of the type b(m)+m*b(m-1), where b is a polygonal number: A006003, A069778, A143690, A204674, A212133, A226449, A226451. Sequence in context: A229395 A306965 A045852 * A105938 A342254 A226254 Adjacent sequences:  A226447 A226448 A226449 * A226451 A226452 A226453 KEYWORD nonn,easy AUTHOR Bruno Berselli, Jun 07 2013 STATUS approved

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Last modified May 7 19:23 EDT 2021. Contains 343652 sequences. (Running on oeis4.)