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A005570 Number of walks on cubic lattice.
(Formerly M5038)
2
17, 50, 99, 164, 245, 342, 455, 584, 729, 890, 1067, 1260, 1469, 1694, 1935, 2192, 2465, 2754, 3059, 3380, 3717, 4070, 4439, 4824, 5225, 5642, 6075, 6524, 6989, 7470, 7967, 8480, 9009, 9554, 10115, 10692, 11285 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Partial sums of A158057.

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Jeremy Gardiner, Table of n, a(n) for n = 1..999

R. K. Guy, Letter to N. J. A. Sloane, May 1990

R. K. Guy, Catwalks, sandsteps and Pascal pyramids, J. Integer Sequences, Vol. 3 (2000), Article #00.1.6 (see figure 7).

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(n) = 8*n^2 + 9*n.

G.f.: (17-x)/(1-x)^3. Simon Plouffe in his 1992 dissertation.

a(n) = 16 * A000217(n) + n. - Jon Perry, Nov 05 2014

MATHEMATICA

CoefficientList[Series[(17 - x) / (1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Nov 05 2014 *)

PROG

(PARI) Vec((17-x)/(1-x)^3 + O(x^50)) \\ Michel Marcus, Nov 05 2014

(MAGMA) [8*n^2 + 9*n : n in [1..40]]; // Vincenzo Librandi, Nov 05 2014

CROSSREFS

Sequence in context: A098329 A160076 A003124 * A195037 A214660 A258598

Adjacent sequences:  A005567 A005568 A005569 * A005571 A005572 A005573

KEYWORD

nonn,walk,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

Formula and more terms from Jeffrey Shallit, Aug 15 1995

STATUS

approved

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Last modified January 22 09:52 EST 2019. Contains 319363 sequences. (Running on oeis4.)