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 A226488 a(n) = n*(13*n-9)/2. 22
 0, 2, 17, 45, 86, 140, 207, 287, 380, 486, 605, 737, 882, 1040, 1211, 1395, 1592, 1802, 2025, 2261, 2510, 2772, 3047, 3335, 3636, 3950, 4277, 4617, 4970, 5336, 5715, 6107, 6512, 6930, 7361, 7805, 8262, 8732, 9215, 9711, 10220, 10742, 11277, 11825, 12386, 12960 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Sum of n-th octagonal number and n-th 9-gonal (nonagonal) number. Sum of reciprocals of a(n), for n>0: 0.629618994194109711163742089971688... 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 G.f.: x*(2+11*x)/(1-x)^3. a(n) + a(-n) = A152742(n). a(0)=0, a(1)=2, a(2)=17; for n>2, a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, Jun 19 2013 MAPLE A226488:=n->n*(13*n - 9)/2; seq(A226488(n), n=0..50); # Wesley Ivan Hurt, Feb 25 2014 MATHEMATICA Table[n (13 n - 9)/2, {n, 0, 50}] LinearRecurrence[{3, -3, 1}, {0, 2, 17}, 50] (* Harvey P. Dale, Jun 19 2013 *) CoefficientList[Series[x (2 + 11 x)/(1 - x)^3, {x, 0, 45}], x] (* Vincenzo Librandi, Aug 18 2013 *) PROG (MAGMA) [n*(13*n-9)/2: n in [0..50]]; (MAGMA) I:=[0, 2, 17]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // Vincenzo Librandi, Aug 18 2013 (PARI) a(n)=n*(13*n-9)/2 \\ Charles R Greathouse IV, Sep 24 2015 CROSSREFS Cf. A000567, A001106, A153080 (first differences). Cf. numbers of the form n*(n*k-k+4))/2 listed in A005843 (k=0), A000096 (k=1), A002378 (k=2), A005449 (k=3), A001105 (k=4), A005476 (k=5), A049450 (k=6), A218471 (k=7), A002939 (k=8), A062708 (k=9), A135706 (k=10), A180223 (k=11), A139267 (n=12), this sequence (k=13), A139268 (k=14), A226489 (k=15), A139271 (k=16), A180232 (k=17), A152995 (k=18), A226490 (k=19), A152965 (k=20), A226491 (k=21), A152997 (k=22). Sequence in context: A165637 A100271 A046973 * A134784 A023256 A073775 Adjacent sequences:  A226485 A226486 A226487 * A226489 A226490 A226491 KEYWORD nonn,easy AUTHOR Bruno Berselli, Jun 09 2013 STATUS approved

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Last modified July 21 19:25 EDT 2019. Contains 325199 sequences. (Running on oeis4.)