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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
J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
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
Sequence in context: A284506 A157419 A008368 * A060023 A345531 A357644
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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