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 A261391 a(n) = n^5 + 5*n^3 + 5*n. 4
 0, 11, 82, 393, 1364, 3775, 8886, 18557, 35368, 62739, 105050, 167761, 257532, 382343, 551614, 776325, 1069136, 1444507, 1918818, 2510489, 3240100, 4130511, 5206982, 6497293, 8031864, 9843875, 11969386, 14447457, 17320268, 20633239, 24435150, 28778261, 33718432, 39315243, 45632114 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Also numbers of the form (n-th metallic mean)^5 - 1/(n-th metallic mean)^5, see link to Wikipedia. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Wikipedia, Metallic mean. Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1). FORMULA a(n) = ( (n+sqrt(n^2+4))/2 )^5 - 1/( (n+sqrt(n^2+4))/2 )^5. a(n) = -a(-n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6). - Colin Barker, Aug 18 2015 G.f.: x*(11*x^4+16*x^3+66*x^2+16*x+11) / (x-1)^6. - Colin Barker, Aug 18 2015 E.g.f.: (x^5 + 15*x^4 + 70*x^3 + 120*x^2 + 71*x + 11)*e^x. - G. C. Greubel, Aug 21 2015 MATHEMATICA Array[#^5 + 5 #^3 + 5 # &, 34] (* Michael De Vlieger, Aug 18 2015 *) Table[n^5 + 5*n^3 + 5*n, {n, 0, 50}] (* G. C. Greubel, Aug 21 2015 *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 11, 82, 393, 1364, 3775}, 40] (* Harvey P. Dale, May 07 2018 *) PROG (PARI) concat(0, Vec(x*(11*x^4+16*x^3+66*x^2+16*x+11)/(x-1)^6 + O(x^100))) \\ Colin Barker, Aug 18 2015 CROSSREFS Cf. A001622, A014176, A098316, A098317, A098318, A176398, A176439, A176458, A176522. Sequence in context: A085879 A239459 A197643 * A211845 A029887 A026871 Adjacent sequences:  A261388 A261389 A261390 * A261392 A261393 A261394 KEYWORD nonn,easy AUTHOR Raphael Ranna, Aug 17 2015 EXTENSIONS Offset changed from 1 to 0, initial 0 added and b-file adapted from Bruno Berselli, Aug 25 2015 STATUS approved

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Last modified June 14 05:51 EDT 2021. Contains 345018 sequences. (Running on oeis4.)