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 A164845 a(n) = (6 + 10*n + 5*n^2 + n^3)/2. 4
 3, 11, 27, 54, 95, 153, 231, 332, 459, 615, 803, 1026, 1287, 1589, 1935, 2328, 2771, 3267, 3819, 4430, 5103, 5841, 6647, 7524, 8475, 9503, 10611, 11802, 13079, 14445, 15903, 17456, 19107, 20859, 22715, 24678, 26751, 28937, 31239, 33660, 36203, 38871 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Row sums of the triangle defined by non-interrupted runs in A080036. If the sequence of integers is split at positions defined by A000124 we obtain A080036. Its runs of consecutive integers can be placed into rows of a triangle:     3;     5,  6;     8,  9, 10;    12, 13, 14, 15;    17, 18, 19, 20, 21;    ... The a(n) are the row sums of this triangle. The a(n) are also the binomial transform of the quasi-finite sequence 3, 8, 8, 3, 0 (0 continued). An associated integer sequence could be defined by a(n)/A026741(n+1) = 3, 11, 9, 27, ... LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA a(n) = A162607(n+3) + n. First differences: a(n+1) - a(n) = A104249(n+2), i.e., a(n) = a(n-1) + 3*n^2/2 + 7*n/2 +3. Second differences: a(n+2) - 2*a(n+1) + a(n) = A016789(n+2). a(n) = 2*a(n-1) - a(n-2) + 3*n + 5, n>1. a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + 3, n>2. a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4), n>3. G.f.: (3-x+x^2)/(x-1)^4. E.g.f.: (6 + 16*x + 8*x^2 + x^3)*exp(x)/2. - G. C. Greubel, Apr 21 2018 MATHEMATICA Table[(6 + 10*n + 5*n^2 + n^3)/2, {n, 0, 50}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {3, 11, 27, 54}, 50] (* G. C. Greubel, Apr 21 2018 *) PROG (MAGMA) [3+5*n+5*n^2/2+n^3/2: n in [0..50]]; // Vincenzo Librandi, Aug 07 2011 (PARI) for(n=0, 50, print1((6+10*n+5*n^2+n^3)/2, ", ")) \\ G. C. Greubel, Apr 21 2018 CROSSREFS Cf. A135278. Sequence in context: A170945 A164897 A212982 * A024194 A011941 A219621 Adjacent sequences:  A164842 A164843 A164844 * A164846 A164847 A164848 KEYWORD nonn,easy AUTHOR Paul Curtz, Aug 28 2009 EXTENSIONS Edited and extended by R. J. Mathar, Aug 31 2009 Corrected typo in recurrence, observed by Paul Curtz - R. J. Mathar, Sep 25 2009 STATUS approved

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Last modified May 12 09:53 EDT 2021. Contains 343821 sequences. (Running on oeis4.)