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A005571 Number of walks on cubic lattice.
(Formerly M5352)
0
76, 288, 700, 1376, 2380, 3776, 5628, 8000, 10956, 14560, 18876, 23968, 29900, 36736, 44540, 53376, 63308, 74400, 86716, 100320, 115276, 131648, 149500, 168896, 189900, 212576, 236988, 263200, 291276, 321280, 353276, 387328, 423500, 461856, 502460, 545376 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

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

LINKS

Table of n, a(n) for n=0..35.

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

Richard 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; arXiv:0911.4975 [math.NT], 2009.

Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

G.f.: 4*(19-4*x+x^2)/(x-1)^4. - Simon Plouffe in his 1992 dissertation

a(n) = 4(n+1)(n+3)(8n+19)/3.

Sum_{n>=0} 1/a(n) = 499/1936 + (6*log(1+sqrt(2))*sqrt(2) - 3*(sqrt(2)-1)*Pi - 24*log(2))/55. - Amiram Eldar, Sep 10 2022

MATHEMATICA

a[n_] := 4 (n + 1) (n + 3) (8 n + 19)/3; Array[a, 30, 0] (* Amiram Eldar, Sep 10 2022 *)

PROG

(PARI) vector(40, n, n--; 4*(n+1)*(n+3)*(8*n+19)/3) \\ Michel Marcus, Oct 13 2014

CROSSREFS

Sequence in context: A251078 A153676 A060316 * A233877 A067987 A167586

Adjacent sequences: A005568 A005569 A005570 * A005572 A005573 A005574

KEYWORD

nonn,walk,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 30 11:57 EST 2022. Contains 358441 sequences. (Running on oeis4.)