The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A023054 Simon Plouffe's conjectured extension of sequence A008368. 2
 1, 1, 3, 4, 7, 8, 13, 14, 20, 22, 29, 31, 40, 42, 52, 55, 66, 69, 82, 85, 99, 103, 118, 122, 139, 143, 161, 166, 185, 190, 211, 216, 238, 244, 267, 273, 298, 304, 330, 337, 364, 371, 400, 407, 437, 445, 476, 484, 517, 525, 559, 568, 603, 612, 649, 658, 696, 706, 745, 755 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..59. J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf). Index entries for linear recurrences with constant coefficients, signature (0,2,1,-1,-2,0,1). FORMULA G.f.: (1-x^5)/((1-x)*(1-x^2)^2*(1-x^3)). Euler transform of length 5 sequence [ 1, 2, 1, 0, -1]. - Michael Somos, May 22 2014 a(-3 - n) = a(n). - Michael Somos, May 22 2014 a(2*n + 2) - a(2*n) = A032793(n + 2). a(2*n + 3) - a(2*n + 1) = A042706(n + 2). - Michael Somos, May 22 2014 EXAMPLE G.f. = 1 + x + 3*x^2 + 4*x^3 + 7*x^4 + 8*x^5 + 13*x^6 + 14*x^7 + 20*x^8 + ... MATHEMATICA CoefficientList[Series[(1-x^5)/((1-x)*(1-x^2)^2*(1-x^3)), {x, 0, 59}], x] (* Georg Fischer, Oct 13 2020 *) PROG (PARI) {a(n) = if( n%2, (n + 1) * (5*n + 7) + 8 * (n%6 == 3), (n + 2) * (5*n + 8) + 8 * (n%6 == 0) ) / 24}; /* Michael Somos, May 22 2014 */ (PARI) {a(n) = if( n<0, n = -3 - n); polcoeff( (1 - x^5) / ((1 - x) * (1 - x^2)^2 * (1 - x^3)) + x * O(x^n), n)}; /* Michael Somos, May 22 2014 */ CROSSREFS Cf. A032793, A042706. Sequence in context: A284506 A157419 A008368 * A060023 A345531 A357644 Adjacent sequences: A023051 A023052 A023053 * A023055 A023056 A023057 KEYWORD nonn,easy AUTHOR N. J. A. Sloane and J. H. Conway STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 14 19:19 EDT 2024. Contains 373401 sequences. (Running on oeis4.)