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 A162460 First differences of A161762. 1
 0, 2, 2, 7, 14, 37, 90, 232, 594, 1541, 4004, 10441, 27260, 71254, 186354, 487579, 1276002, 3339821, 8742470, 22885996, 59912930, 156848617, 410626152, 1075018897, 2814412824, 7368190922, 19290113570, 50502074767, 132215989334, 346145696821, 906220783314 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (3,1,-5,-1,1). FORMULA a(n) = A161762(n+1) - A161762(n). a(n) = A000217(A000045(n+1)) + A000217(A000045(n-1)-1) - A000290(A000045(n)). - R. J. Mathar, Jul 06 2009 From Colin Barker, Feb 25 2019: (Start) G.f.: x^2*(2 - 4*x - x^2 + x^3) / ((1 + x)*(1 - 3*x + x^2)*(1 - x - x^2)). a(n) = 3*a(n-1) + a(n-2) - 5*a(n-3) - a(n-4) + a(n-5) for n>4. (End) EXAMPLE a(1) = 0 = 1 - 1. a(2) = 2 = 3 - 1. a(3) = 2 = 5 - 3. a(4) = 7 = 12 - 5. a(5) = 14 = 26 - 12. a(6) = 37 = 63 - 26. MAPLE A000217 := proc(n) n*(n+1)/2 ; end: A000045 := proc(n) combinat[fibonacci](n) ; end: A162460 := proc(n) A161762(n+1)-A161762(n) ; end: A161762 := proc(n) A000217(A000045(n))-A000217( A000045(n-1)-1) ; end: seq(A162460(n), n=1..80) ; # R. J. Mathar, Jul 06 2009 PROG (PARI) concat(0, Vec(x^2*(2 - 4*x - x^2 + x^3) / ((1 + x)*(1 - 3*x + x^2)*(1 - x - x^2)) + O(x^40))) \\ Colin Barker, Feb 25 2019 CROSSREFS Cf. A000045, A161762. Sequence in context: A344048 A228432 A298959 * A187306 A061274 A061575 Adjacent sequences: A162457 A162458 A162459 * A162461 A162462 A162463 KEYWORD nonn,easy AUTHOR Juri-Stepan Gerasimov, Jul 04 2009 EXTENSIONS a(21) corrected by R. J. Mathar, Jul 05 2009 STATUS approved

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Last modified April 16 03:28 EDT 2024. Contains 371696 sequences. (Running on oeis4.)