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 A279895 a(n) = n*(5*n + 11)/2. 2
 0, 8, 21, 39, 62, 90, 123, 161, 204, 252, 305, 363, 426, 494, 567, 645, 728, 816, 909, 1007, 1110, 1218, 1331, 1449, 1572, 1700, 1833, 1971, 2114, 2262, 2415, 2573, 2736, 2904, 3077, 3255, 3438, 3626, 3819, 4017, 4220, 4428, 4641, 4859, 5082, 5310, 5543, 5781, 6024, 6272, 6525 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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 O.g.f.: x*(8 - 3*x)/(1 - x)^3. E.g.f.: x*(16 + 5*x)*exp(x)/2. a(n+h) - a(n-h) = h*A017281(n+1), with h>=0. A particular case: a(n) - a(-n) = 11*n = A008593(n). a(n+h) + a(n-h) = 2*a(n) + A033429(h), with h>=0. A particular case: a(n) + a(-n) = A033429(n). a(n) - a(n-2) = A017281(n) for n>1. Also: 40*a(n) + 121 = A017281(n+1)^2. a(n) = A000566(n) + 7*n, also a(n) = A000566(n) + A008589(n). - Michel Marcus, Dec 22 2016 MATHEMATICA Table[n (5 n + 11)/2, {n, 0, 60}] PROG (PARI) vector(60, n, n--; n*(5*n+11)/2) (Python) [n*(5*n+11)/2 for n in range(60)] (Sage) [n*(5*n+11)/2 for n in range(60)] (MAGMA) [n*(5*n+11)/2: n in [0..60]]; CROSSREFS Cf. A000566, A008589, A017281. Second bisection of A165720. The first differences are in A016885. Cf. similar sequences provided by P(s,m)+s*m, where P(s,m) = ((s-2)*m^2-(s-4)*m)/2 is the m-th s-gonal number: A008585 (s=2), A055999 (s=3), A028347 (s=4), A140091 (s=5), A033537 (s=6), this sequence (s=7), A067725 (s=8). Sequence in context: A241986 A179681 A224039 * A225287 A000567 A124484 Adjacent sequences:  A279892 A279893 A279894 * A279896 A279897 A279898 KEYWORD nonn,easy AUTHOR Bruno Berselli, Dec 22 2016 STATUS approved

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Last modified May 10 04:59 EDT 2021. Contains 343748 sequences. (Running on oeis4.)