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 A009947 Sequence of nonnegative integers, but insert n/2 after every even number n. 15
 0, 0, 1, 2, 1, 3, 4, 2, 5, 6, 3, 7, 8, 4, 9, 10, 5, 11, 12, 6, 13, 14, 7, 15, 16, 8, 17, 18, 9, 19, 20, 10, 21, 22, 11, 23, 24, 12, 25, 26, 13, 27, 28, 14, 29, 30, 15, 31, 32, 16, 33, 34, 17, 35, 36, 18, 37, 38, 19, 39, 40, 20, 41, 42, 21, 43, 44, 22, 45, 46 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Coefficients in expansion of e/3 = Sum_{n>=1} a(n)/n!, using greedy algorithm. Numerators of Peirce sequence of order 2. REFERENCES R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, Reading, MA, 2nd ed. 1998, p. 151. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1). FORMULA G.f.: x^2*(x^3+x^2+2*x+1) / ((x-1)^2*(x^2+x+1)^2). - Colin Barker, Aug 31 2013 a(n) = (n^2-n+floor(n/3)*(18*floor(n/3)^2-3*(4*n-7)*floor(n/3)+2*n^2-10*n+7))/2. - Luce ETIENNE, Mar 29 2017 MAPLE A009947 := proc(a, n) local i, b, c; b := a; c := [ floor(b) ]; for i from 1 to n-1 do b := b-c[ i ]/i!; c := [ op(c), floor(b*(i+1)!) ]; od; c; end: MATHEMATICA Flatten[Table[If[EvenQ[n], {n, n/2}, n], {n, 0, 40}]] (* Harvey P. Dale, Feb 17 2016 *) PROG (Haskell) a009947 n = a009947_list !! n a009947_list = concatMap (\x -> [2 * x, x, 2 * x + 1]) [0..] -- Reinhard Zumkeller, Jul 06 2012 (PARI) a(n)=if(n%3==1, n\3, n\3*2+!!(n%3)) \\ Charles R Greathouse IV, Sep 02 2015 (PARI) concat(vector(2), Vec(x^2*(x^3+x^2+2*x+1) / ((x-1)^2*(x^2+x+1)^2) + O(x^100))) \\ Colin Barker, Mar 29 2017 CROSSREFS Cf. A071281, A214090 (parity), A001477. Sequence in context: A112382 A117384 A125160 * A166711 A026249 A130527 Adjacent sequences:  A009944 A009945 A009946 * A009948 A009949 A009950 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified May 17 22:15 EDT 2021. Contains 343992 sequences. (Running on oeis4.)